id sid tid token lemma pos cet-3919 1 1 chemical chemical NOUN cet-3919 1 2 engineering engineering NOUN cet-3919 1 3 transactions transaction NOUN cet-3919 1 4 vol vol NOUN cet-3919 1 5 . . PROPN cet-3919 2 1 51 51 NUM cet-3919 2 2 , , PUNCT cet-3919 2 3 2016 2016 NUM cet-3919 2 4 a a DET cet-3919 2 5 publication publication NOUN cet-3919 2 6 of of ADP cet-3919 2 7 the the DET cet-3919 2 8 italian italian ADJ cet-3919 2 9 association association NOUN cet-3919 2 10 of of ADP cet-3919 2 11 chemical chemical PROPN cet-3919 2 12 engineering engineering NOUN cet-3919 2 13 online online ADV cet-3919 2 14 at at ADP cet-3919 2 15 www.aidic.it/cet www.aidic.it/cet PROPN cet-3919 2 16 guest guest NOUN cet-3919 2 17 editors editor NOUN cet-3919 2 18 : : PUNCT cet-3919 2 19 tichun tichun PROPN cet-3919 2 20 wang wang PROPN cet-3919 2 21 , , PUNCT cet-3919 2 22 hongyang hongyang PROPN cet-3919 2 23 zhang zhang PROPN cet-3919 2 24 , , PUNCT cet-3919 2 25 lei lei PROPN cet-3919 2 26 tian tian ADJ cet-3919 2 27 copyright copyright NOUN cet-3919 2 28 © © PROPN cet-3919 2 29 2016 2016 NUM cet-3919 2 30 , , PUNCT cet-3919 2 31 aidic aidic ADJ cet-3919 2 32 servizi servizi PROPN cet-3919 2 33 s.r.l s.r.l NOUN cet-3919 2 34 . . PUNCT cet-3919 2 35 , , PUNCT cet-3919 2 36 isbn isbn PROPN cet-3919 2 37 978 978 NUM cet-3919 2 38 - - SYM cet-3919 2 39 88 88 NUM cet-3919 2 40 - - PUNCT cet-3919 2 41 95608 95608 NUM cet-3919 2 42 - - PUNCT cet-3919 2 43 43 43 NUM cet-3919 2 44 - - SYM cet-3919 2 45 3 3 NUM cet-3919 2 46 ; ; PUNCT cet-3919 2 47 issn issn PROPN cet-3919 2 48 2283 2283 NUM cet-3919 2 49 - - SYM cet-3919 2 50 9216 9216 NUM cet-3919 2 51 proof proof NOUN cet-3919 2 52 of of ADP cet-3919 2 53 lagrange lagrange PROPN cet-3919 2 54 mean mean NOUN cet-3919 2 55 value value NOUN cet-3919 2 56 theorem theorem NOUN cet-3919 2 57 and and CCONJ cet-3919 2 58 its its PRON cet-3919 2 59 application application NOUN cet-3919 2 60 in in ADP cet-3919 2 61 text text NOUN cet-3919 2 62 design design NOUN cet-3919 2 63 jianhua jianhua PROPN cet-3919 2 64 li li PROPN cet-3919 2 65 mathematical mathematical PROPN cet-3919 2 66 science science PROPN cet-3919 2 67 college college PROPN cet-3919 2 68 , , PUNCT cet-3919 2 69 luoyang luoyang PROPN cet-3919 2 70 normal normal PROPN cet-3919 2 71 university university PROPN cet-3919 2 72 , , PUNCT cet-3919 2 73 luoyang luoyang PROPN cet-3919 2 74 , , PUNCT cet-3919 2 75 471000 471000 NUM cet-3919 2 76 , , PUNCT cet-3919 2 77 p.r.china p.r.china NOUN cet-3919 2 78 ljhly2010@163.com ljhly2010@163.com PROPN cet-3919 2 79 at at ADP cet-3919 2 80 present present ADJ cet-3919 2 81 , , PUNCT cet-3919 2 82 there there PRON cet-3919 2 83 are be VERB cet-3919 2 84 a a DET cet-3919 2 85 lot lot NOUN cet-3919 2 86 of of ADP cet-3919 2 87 papers paper NOUN cet-3919 2 88 on on ADP cet-3919 2 89 lagrange lagrange PROPN cet-3919 2 90 mean mean NOUN cet-3919 2 91 value value NOUN cet-3919 2 92 theorem theorem ADJ cet-3919 2 93 proving prove VERB cet-3919 2 94 method method NOUN cet-3919 2 95 , , PUNCT cet-3919 2 96 the the DET cet-3919 2 97 paper paper NOUN cet-3919 2 98 on on ADP cet-3919 2 99 the the DET cet-3919 2 100 application application NOUN cet-3919 2 101 of of ADP cet-3919 2 102 the the DET cet-3919 2 103 theorem theorem NOUN cet-3919 2 104 is be AUX cet-3919 2 105 not not PART cet-3919 2 106 in in ADP cet-3919 2 107 a a DET cet-3919 2 108 few few ADJ cet-3919 2 109 , , PUNCT cet-3919 2 110 but but CCONJ cet-3919 2 111 text text NOUN cet-3919 2 112 designs design NOUN cet-3919 2 113 from from ADP cet-3919 2 114 the the DET cet-3919 2 115 perspective perspective NOUN cet-3919 2 116 of of ADP cet-3919 2 117 curriculum curriculum NOUN cet-3919 2 118 explore explore VERB cet-3919 2 119 proving prove VERB cet-3919 2 120 a a DET cet-3919 2 121 theorem theorem NOUN cet-3919 2 122 and and CCONJ cet-3919 2 123 its its PRON cet-3919 2 124 application application NOUN cet-3919 2 125 to to ADP cet-3919 2 126 the the DET cet-3919 2 127 design design NOUN cet-3919 2 128 of of ADP cet-3919 2 129 a a DET cet-3919 2 130 text text NOUN cet-3919 2 131 are be AUX cet-3919 2 132 rare rare ADJ cet-3919 2 133 . . PUNCT cet-3919 3 1 this this DET cet-3919 3 2 paper paper NOUN cet-3919 3 3 first first ADV cet-3919 3 4 analyzes analyze VERB cet-3919 3 5 the the DET cet-3919 3 6 objectives objective NOUN cet-3919 3 7 , , PUNCT cet-3919 3 8 tasks task NOUN cet-3919 3 9 , , PUNCT cet-3919 3 10 methods method NOUN cet-3919 3 11 , , PUNCT cet-3919 3 12 and and CCONJ cet-3919 3 13 then then ADV cet-3919 3 14 focuses focus VERB cet-3919 3 15 on on ADP cet-3919 3 16 the the DET cet-3919 3 17 teaching teaching NOUN cet-3919 3 18 strategies strategy NOUN cet-3919 3 19 and and CCONJ cet-3919 3 20 processes process NOUN cet-3919 3 21 , , PUNCT cet-3919 3 22 finally finally ADV cet-3919 3 23 , , PUNCT cet-3919 3 24 it it PRON cet-3919 3 25 comes come VERB cet-3919 3 26 to to ADP cet-3919 3 27 the the DET cet-3919 3 28 reflection reflection NOUN cet-3919 3 29 , , PUNCT cet-3919 3 30 thus thus ADV cet-3919 3 31 forming form VERB cet-3919 3 32 a a DET cet-3919 3 33 complete complete ADJ cet-3919 3 34 , , PUNCT cet-3919 3 35 detailed detailed ADJ cet-3919 3 36 and and CCONJ cet-3919 3 37 full full ADJ cet-3919 3 38 text text NOUN cet-3919 3 39 design design NOUN cet-3919 3 40 on on ADP cet-3919 3 41 the the DET cet-3919 3 42 proof proof NOUN cet-3919 3 43 of of ADP cet-3919 3 44 lagrange lagrange PROPN cet-3919 3 45 mean mean NOUN cet-3919 3 46 value value NOUN cet-3919 3 47 theorem theorem NOUN cet-3919 3 48 and and CCONJ cet-3919 3 49 its its PRON cet-3919 3 50 application application NOUN cet-3919 3 51 . . PUNCT cet-3919 4 1 in in ADP cet-3919 4 2 this this DET cet-3919 4 3 paper paper NOUN cet-3919 4 4 , , PUNCT cet-3919 4 5 through through ADP cet-3919 4 6 study study NOUN cet-3919 4 7 of of ADP cet-3919 4 8 the the DET cet-3919 4 9 teaching teaching NOUN cet-3919 4 10 content content NOUN cet-3919 4 11 of of ADP cet-3919 4 12 the the DET cet-3919 4 13 lagrange lagrange PROPN cet-3919 4 14 mean mean NOUN cet-3919 4 15 value value NOUN cet-3919 4 16 theorem theorem VERB cet-3919 4 17 , , PUNCT cet-3919 4 18 optimizing optimize VERB cet-3919 4 19 the the DET cet-3919 4 20 teaching teaching NOUN cet-3919 4 21 design design NOUN cet-3919 4 22 , , PUNCT cet-3919 4 23 adopting adopt VERB cet-3919 4 24 it it PRON cet-3919 4 25 in in ADP cet-3919 4 26 the the DET cet-3919 4 27 classroom classroom NOUN cet-3919 4 28 teaching teaching NOUN cet-3919 4 29 , , PUNCT cet-3919 4 30 the the DET cet-3919 4 31 paper paper NOUN cet-3919 4 32 gives give VERB cet-3919 4 33 the the DET cet-3919 4 34 classroom classroom NOUN cet-3919 4 35 teaching teaching NOUN cet-3919 4 36 practice practice NOUN cet-3919 4 37 in in ADP cet-3919 4 38 the the DET cet-3919 4 39 specific specific ADJ cet-3919 4 40 practices practice NOUN cet-3919 4 41 , , PUNCT cet-3919 4 42 thereby thereby ADV cet-3919 4 43 improves improve VERB cet-3919 4 44 the the DET cet-3919 4 45 effect effect NOUN cet-3919 4 46 of of ADP cet-3919 4 47 classroom classroom NOUN cet-3919 4 48 teaching teaching NOUN cet-3919 4 49 , , PUNCT cet-3919 4 50 and and CCONJ cet-3919 4 51 it it PRON cet-3919 4 52 has have VERB cet-3919 4 53 a a DET cet-3919 4 54 strong strong ADJ cet-3919 4 55 guiding guiding NOUN cet-3919 4 56 significance significance NOUN cet-3919 4 57 in in ADP cet-3919 4 58 theory theory NOUN cet-3919 4 59 and and CCONJ cet-3919 4 60 practice practice NOUN cet-3919 4 61 . . PUNCT cet-3919 5 1 1 1 X cet-3919 5 2 . . X cet-3919 5 3 introduction introduction NOUN cet-3919 5 4 the the DET cet-3919 5 5 differential differential ADJ cet-3919 5 6 mean mean NOUN cet-3919 5 7 value value NOUN cet-3919 5 8 theorem theorem NOUN cet-3919 5 9 is be AUX cet-3919 5 10 the the DET cet-3919 5 11 theoretical theoretical ADJ cet-3919 5 12 basis basis NOUN cet-3919 5 13 of of ADP cet-3919 5 14 the the DET cet-3919 5 15 application application NOUN cet-3919 5 16 of of ADP cet-3919 5 17 the the DET cet-3919 5 18 derivative derivative NOUN cet-3919 5 19 , , PUNCT cet-3919 5 20 which which PRON cet-3919 5 21 is be AUX cet-3919 5 22 the the DET cet-3919 5 23 bridge bridge NOUN cet-3919 5 24 between between ADP cet-3919 5 25 the the DET cet-3919 5 26 function function NOUN cet-3919 5 27 and and CCONJ cet-3919 5 28 its its PRON cet-3919 5 29 derivative derivative NOUN cet-3919 5 30 . . PUNCT cet-3919 6 1 it it PRON cet-3919 6 2 is be AUX cet-3919 6 3 an an DET cet-3919 6 4 important important ADJ cet-3919 6 5 tool tool NOUN cet-3919 6 6 to to PART cet-3919 6 7 study study VERB cet-3919 6 8 the the DET cet-3919 6 9 function function NOUN cet-3919 6 10 overall overall ADV cet-3919 6 11 by by ADP cet-3919 6 12 using use VERB cet-3919 6 13 derivative derivative NOUN cet-3919 6 14 of of ADP cet-3919 6 15 the the DET cet-3919 6 16 locality locality NOUN cet-3919 6 17 , , PUNCT cet-3919 6 18 and and CCONJ cet-3919 6 19 forms form VERB cet-3919 6 20 a a DET cet-3919 6 21 relation relation NOUN cet-3919 6 22 between between ADP cet-3919 6 23 the the DET cet-3919 6 24 increment increment NOUN cet-3919 6 25 of of ADP cet-3919 6 26 a a DET cet-3919 6 27 function function NOUN cet-3919 6 28 on on ADP cet-3919 6 29 an an DET cet-3919 6 30 interval interval NOUN cet-3919 6 31 and and CCONJ cet-3919 6 32 the the DET cet-3919 6 33 derivative derivative NOUN cet-3919 6 34 of of ADP cet-3919 6 35 the the DET cet-3919 6 36 function function NOUN cet-3919 6 37 at at ADP cet-3919 6 38 a a DET cet-3919 6 39 specific specific ADJ cet-3919 6 40 point point NOUN cet-3919 6 41 of of ADP cet-3919 6 42 the the DET cet-3919 6 43 interval interval NOUN cet-3919 6 44 . . PUNCT cet-3919 7 1 as as ADP cet-3919 7 2 a a DET cet-3919 7 3 result result NOUN cet-3919 7 4 , , PUNCT cet-3919 7 5 differential differential ADJ cet-3919 7 6 mean mean NOUN cet-3919 7 7 value value NOUN cet-3919 7 8 theorem theorem NOUN cet-3919 7 9 has have VERB cet-3919 7 10 important important ADJ cet-3919 7 11 theoretical theoretical ADJ cet-3919 7 12 significance significance NOUN cet-3919 7 13 and and CCONJ cet-3919 7 14 application application NOUN cet-3919 7 15 value value NOUN cet-3919 7 16 . . PUNCT cet-3919 8 1 2 2 X cet-3919 8 2 . . X cet-3919 8 3 main main ADJ cet-3919 8 4 text text NOUN cet-3919 8 5 2.1 2.1 NUM cet-3919 8 6 task task NOUN cet-3919 8 7 analysis analysis NOUN cet-3919 8 8 " " PUNCT cet-3919 8 9 lagrange lagrange NOUN cet-3919 8 10 mean mean NOUN cet-3919 8 11 value value NOUN cet-3919 8 12 theorem theorem NOUN cet-3919 8 13 and and CCONJ cet-3919 8 14 its its PRON cet-3919 8 15 application application NOUN cet-3919 8 16 " " PUNCT cet-3919 8 17 belongs belong VERB cet-3919 8 18 to to ADP cet-3919 8 19 the the DET cet-3919 8 20 first first ADJ cet-3919 8 21 section section NOUN cet-3919 8 22 of of ADP cet-3919 8 23 the the DET cet-3919 8 24 third third ADJ cet-3919 8 25 chapter chapter NOUN cet-3919 8 26 numbering number VERB cet-3919 8 27 in in ADP cet-3919 8 28 the the DET cet-3919 8 29 first first ADJ cet-3919 8 30 volume volume NOUN cet-3919 8 31 of of ADP cet-3919 8 32 " " PUNCT cet-3919 8 33 higher high ADJ cet-3919 8 34 mathematics mathematic NOUN cet-3919 8 35 " " PUNCT cet-3919 8 36 ( ( PUNCT cet-3919 8 37 6th 6th NOUN cet-3919 8 38 edition edition NOUN cet-3919 8 39 ) ) PUNCT cet-3919 8 40 ( ( PUNCT cet-3919 8 41 department department NOUN cet-3919 8 42 of of ADP cet-3919 8 43 mathematics mathematic NOUN cet-3919 8 44 , , PUNCT cet-3919 8 45 tongji tongji PROPN cet-3919 8 46 university university NOUN cet-3919 8 47 , , PUNCT cet-3919 8 48 higher high ADJ cet-3919 8 49 education education NOUN cet-3919 8 50 press press NOUN cet-3919 8 51 ) ) PUNCT cet-3919 8 52 , , PUNCT cet-3919 8 53 the the DET cet-3919 8 54 third third ADJ cet-3919 8 55 chapter chapter NOUN cet-3919 8 56 is be AUX cet-3919 8 57 the the DET cet-3919 8 58 application application NOUN cet-3919 8 59 of of ADP cet-3919 8 60 the the DET cet-3919 8 61 differential differential ADJ cet-3919 8 62 mean mean NOUN cet-3919 8 63 value value NOUN cet-3919 8 64 theorem theorem NOUN cet-3919 8 65 and and CCONJ cet-3919 8 66 the the DET cet-3919 8 67 derivative derivative NOUN cet-3919 8 68 . . PUNCT cet-3919 9 1 the the DET cet-3919 9 2 content content NOUN cet-3919 9 3 of of ADP cet-3919 9 4 this this DET cet-3919 9 5 chapter chapter NOUN cet-3919 9 6 is be AUX cet-3919 9 7 the the DET cet-3919 9 8 continuation continuation NOUN cet-3919 9 9 of of ADP cet-3919 9 10 the the DET cet-3919 9 11 last last ADJ cet-3919 9 12 chapter chapter NOUN cet-3919 9 13 . . PUNCT cet-3919 10 1 it it PRON cet-3919 10 2 mainly mainly ADV cet-3919 10 3 analyzes analyze VERB cet-3919 10 4 and and CCONJ cet-3919 10 5 studies study NOUN cet-3919 10 6 the the DET cet-3919 10 7 character character NOUN cet-3919 10 8 of of ADP cet-3919 10 9 function function NOUN cet-3919 10 10 and and CCONJ cet-3919 10 11 its its PRON cet-3919 10 12 graph graph NOUN cet-3919 10 13 and and CCONJ cet-3919 10 14 various various ADJ cet-3919 10 15 forms form NOUN cet-3919 10 16 by by ADP cet-3919 10 17 using use VERB cet-3919 10 18 derivative derivative ADJ cet-3919 10 19 and and CCONJ cet-3919 10 20 differential differential ADJ cet-3919 10 21 ( ( PUNCT cet-3919 10 22 farid farid ADJ cet-3919 10 23 , , PUNCT cet-3919 10 24 2015 2015 NUM cet-3919 10 25 ) ) PUNCT cet-3919 10 26 . . PUNCT cet-3919 11 1 the the DET cet-3919 11 2 theoretical theoretical ADJ cet-3919 11 3 basis basis NOUN cet-3919 11 4 of of ADP cet-3919 11 5 all all PRON cet-3919 11 6 of of ADP cet-3919 11 7 this this PRON cet-3919 11 8 is be AUX cet-3919 11 9 the the DET cet-3919 11 10 differential differential ADJ cet-3919 11 11 mean mean NOUN cet-3919 11 12 value value NOUN cet-3919 11 13 theorem theorem VERB cet-3919 11 14 , , PUNCT cet-3919 11 15 which which PRON cet-3919 11 16 plays play VERB cet-3919 11 17 an an DET cet-3919 11 18 important important ADJ cet-3919 11 19 role role NOUN cet-3919 11 20 in in ADP cet-3919 11 21 the the DET cet-3919 11 22 differential differential ADJ cet-3919 11 23 calculus calculus NOUN cet-3919 11 24 , , PUNCT cet-3919 11 25 is be AUX cet-3919 11 26 also also ADV cet-3919 11 27 the the DET cet-3919 11 28 content content NOUN cet-3919 11 29 of of ADP cet-3919 11 30 the the DET cet-3919 11 31 first first ADJ cet-3919 11 32 section section NOUN cet-3919 11 33 ( ( PUNCT cet-3919 11 34 zhang zhang PROPN cet-3919 11 35 , , PUNCT cet-3919 11 36 2015 2015 NUM cet-3919 11 37 ) ) PUNCT cet-3919 11 38 . . PUNCT cet-3919 12 1 the the DET cet-3919 12 2 differential differential ADJ cet-3919 12 3 mean mean NOUN cet-3919 12 4 value value NOUN cet-3919 12 5 theorem theorem NOUN cet-3919 12 6 includes include VERB cet-3919 12 7 rolle rolle NOUN cet-3919 12 8 theorem theorem PROPN cet-3919 12 9 , , PUNCT cet-3919 12 10 lagrange lagrange NOUN cet-3919 12 11 mean mean NOUN cet-3919 12 12 value value NOUN cet-3919 12 13 theorem theorem NOUN cet-3919 12 14 , , PUNCT cet-3919 12 15 cauchy cauchy NOUN cet-3919 12 16 mean mean NOUN cet-3919 12 17 value value NOUN cet-3919 12 18 theorem theorem NOUN cet-3919 12 19 and and CCONJ cet-3919 12 20 taylor taylor PROPN cet-3919 12 21 mean mean PROPN cet-3919 12 22 value value NOUN cet-3919 12 23 theorem theorem VERB cet-3919 12 24 . . PUNCT cet-3919 13 1 in in ADP cet-3919 13 2 the the DET cet-3919 13 3 process process NOUN cet-3919 13 4 of of ADP cet-3919 13 5 analysis analysis NOUN cet-3919 13 6 and and CCONJ cet-3919 13 7 demonstration demonstration NOUN cet-3919 13 8 , , PUNCT cet-3919 13 9 the the DET cet-3919 13 10 mean mean ADJ cet-3919 13 11 value value NOUN cet-3919 13 12 theorem theorem NOUN cet-3919 13 13 is be AUX cet-3919 13 14 widely widely ADV cet-3919 13 15 used use VERB cet-3919 13 16 . . PUNCT cet-3919 14 1 the the DET cet-3919 14 2 teaching teaching NOUN cet-3919 14 3 task task NOUN cet-3919 14 4 of of ADP cet-3919 14 5 this this DET cet-3919 14 6 course course NOUN cet-3919 14 7 is be AUX cet-3919 14 8 to to PART cet-3919 14 9 study study VERB cet-3919 14 10 lagrange lagrange NOUN cet-3919 14 11 mean mean NOUN cet-3919 14 12 value value NOUN cet-3919 14 13 theorem theorem NOUN cet-3919 14 14 and and CCONJ cet-3919 14 15 the the DET cet-3919 14 16 application application NOUN cet-3919 14 17 of of ADP cet-3919 14 18 theorem theorem NOUN cet-3919 14 19 in in ADP cet-3919 14 20 equality equality NOUN cet-3919 14 21 and and CCONJ cet-3919 14 22 inequality inequality NOUN cet-3919 14 23 ( ( PUNCT cet-3919 14 24 mortici mortici PROPN cet-3919 14 25 , , PUNCT cet-3919 14 26 2011 2011 NUM cet-3919 14 27 ) ) PUNCT cet-3919 14 28 . . PUNCT cet-3919 15 1 2.2 2.2 NUM cet-3919 15 2 . . PUNCT cet-3919 15 3 objectives objective NOUN cet-3919 15 4 and and CCONJ cet-3919 15 5 basic basic ADJ cet-3919 15 6 requirements requirement NOUN cet-3919 15 7 knowledge knowledge NOUN cet-3919 15 8 and and CCONJ cet-3919 15 9 skill skill NOUN cet-3919 15 10 goals goal NOUN cet-3919 15 11 : : PUNCT cet-3919 15 12 ( ( PUNCT cet-3919 15 13 1 1 X cet-3919 15 14 ) ) PUNCT cet-3919 15 15 through through ADP cet-3919 15 16 the the DET cet-3919 15 17 study study NOUN cet-3919 15 18 of of ADP cet-3919 15 19 this this DET cet-3919 15 20 course course NOUN cet-3919 15 21 , , PUNCT cet-3919 15 22 students student NOUN cet-3919 15 23 should should AUX cet-3919 15 24 understand understand VERB cet-3919 15 25 and and CCONJ cet-3919 15 26 master master VERB cet-3919 15 27 the the DET cet-3919 15 28 conditions condition NOUN cet-3919 15 29 and and CCONJ cet-3919 15 30 conclusions conclusion NOUN cet-3919 15 31 of of ADP cet-3919 15 32 lagrange lagrange PROPN cet-3919 15 33 mean mean NOUN cet-3919 15 34 value value NOUN cet-3919 15 35 theorem theorem VERB cet-3919 15 36 ; ; PUNCT cet-3919 15 37 ( ( PUNCT cet-3919 15 38 2 2 X cet-3919 15 39 ) ) PUNCT cet-3919 15 40 to to PART cet-3919 15 41 make make VERB cet-3919 15 42 the the DET cet-3919 15 43 students student NOUN cet-3919 15 44 understand understand VERB cet-3919 15 45 lagrange lagrange NOUN cet-3919 15 46 mean mean NOUN cet-3919 15 47 value value NOUN cet-3919 15 48 theorem theorem NOUN cet-3919 15 49 and and CCONJ cet-3919 15 50 the the DET cet-3919 15 51 geometric geometric ADJ cet-3919 15 52 meaning meaning NOUN cet-3919 15 53 of of ADP cet-3919 15 54 lagrange lagrange NOUN cet-3919 15 55 mean mean NOUN cet-3919 15 56 value value NOUN cet-3919 15 57 theorem theorem VERB cet-3919 15 58 , , PUNCT cet-3919 15 59 and and CCONJ cet-3919 15 60 the the DET cet-3919 15 61 connection connection NOUN cet-3919 15 62 and and CCONJ cet-3919 15 63 difference difference NOUN cet-3919 15 64 between between ADP cet-3919 15 65 rolle rolle NOUN cet-3919 15 66 theorem theorem PROPN cet-3919 15 67 and and CCONJ cet-3919 15 68 lagrange lagrange PROPN cet-3919 15 69 mean mean NOUN cet-3919 15 70 value value NOUN cet-3919 15 71 theorem theorem VERB cet-3919 15 72 ; ; PUNCT cet-3919 15 73 ( ( PUNCT cet-3919 15 74 3 3 X cet-3919 15 75 ) ) PUNCT cet-3919 15 76 through through ADP cet-3919 15 77 the the DET cet-3919 15 78 study study NOUN cet-3919 15 79 of of ADP cet-3919 15 80 this this DET cet-3919 15 81 course course NOUN cet-3919 15 82 , , PUNCT cet-3919 15 83 students student NOUN cet-3919 15 84 should should AUX cet-3919 15 85 learn learn VERB cet-3919 15 86 how how SCONJ cet-3919 15 87 to to PART cet-3919 15 88 use use VERB cet-3919 15 89 the the DET cet-3919 15 90 mean mean ADJ cet-3919 15 91 value value NOUN cet-3919 15 92 theorem theorem VERB cet-3919 15 93 to to PART cet-3919 15 94 prove prove VERB cet-3919 15 95 the the DET cet-3919 15 96 equality equality NOUN cet-3919 15 97 and and CCONJ cet-3919 15 98 inequality inequality NOUN cet-3919 15 99 . . PUNCT cet-3919 16 1 ability ability NOUN cet-3919 16 2 training train VERB cet-3919 16 3 goal goal NOUN cet-3919 16 4 : : PUNCT cet-3919 16 5 ( ( PUNCT cet-3919 16 6 1 1 X cet-3919 16 7 ) ) PUNCT cet-3919 16 8 to to PART cet-3919 16 9 improve improve VERB cet-3919 16 10 students student NOUN cet-3919 16 11 ’ ' PUNCT cet-3919 16 12 analysis analysis NOUN cet-3919 16 13 ability ability NOUN cet-3919 16 14 and and CCONJ cet-3919 16 15 logical logical ADJ cet-3919 16 16 thinking thinking NOUN cet-3919 16 17 ability ability NOUN cet-3919 16 18 of of ADP cet-3919 16 19 proving prove VERB cet-3919 16 20 mathematical mathematical ADJ cet-3919 16 21 proposition proposition NOUN cet-3919 16 22 with with ADP cet-3919 16 23 the the DET cet-3919 16 24 cycle cycle NOUN cet-3919 16 25 from from ADP cet-3919 16 26 conclusion conclusion NOUN cet-3919 16 27 to to ADP cet-3919 16 28 the the DET cet-3919 16 29 conditions condition NOUN cet-3919 16 30 and and CCONJ cet-3919 16 31 the the DET cet-3919 16 32 conclusion conclusion NOUN cet-3919 16 33 ( ( PUNCT cet-3919 16 34 yi yi NOUN cet-3919 16 35 , , PUNCT cet-3919 16 36 2015 2015 NUM cet-3919 16 37 ) ) PUNCT cet-3919 16 38 . . PUNCT cet-3919 17 1 the the DET cet-3919 17 2 doi doi NOUN cet-3919 17 3 : : PUNCT cet-3919 17 4 10.3303 10.3303 NUM cet-3919 17 5 / / SYM cet-3919 17 6 cet1651055 cet1651055 NOUN cet-3919 17 7 please please INTJ cet-3919 17 8 cite cite VERB cet-3919 17 9 this this DET cet-3919 17 10 article article NOUN cet-3919 17 11 as as ADP cet-3919 17 12 : : PUNCT cet-3919 17 13 li li PROPN cet-3919 17 14 j.h j.h PROPN cet-3919 17 15 . . PROPN cet-3919 17 16 , , PUNCT cet-3919 17 17 2016 2016 NUM cet-3919 17 18 , , PUNCT cet-3919 17 19 proof proof NOUN cet-3919 17 20 of of ADP cet-3919 17 21 lagrange lagrange PROPN cet-3919 17 22 mean mean NOUN cet-3919 17 23 value value NOUN cet-3919 17 24 theorem theorem NOUN cet-3919 17 25 and and CCONJ cet-3919 17 26 its its PRON cet-3919 17 27 application application NOUN cet-3919 17 28 in in ADP cet-3919 17 29 text text NOUN cet-3919 17 30 design design NOUN cet-3919 17 31 , , PUNCT cet-3919 17 32 chemical chemical NOUN cet-3919 17 33 engineering engineering NOUN cet-3919 17 34 transactions transaction NOUN cet-3919 17 35 , , PUNCT cet-3919 17 36 51 51 NUM cet-3919 17 37 , , PUNCT cet-3919 17 38 325 325 NUM cet-3919 17 39 - - SYM cet-3919 17 40 330 330 NUM cet-3919 17 41 doi:10.3303 doi:10.3303 NOUN cet-3919 17 42 / / SYM cet-3919 17 43 cet1651055 cet1651055 NOUN cet-3919 17 44 325 325 NUM cet-3919 17 45 http://scholar.cnki.net/webpress/brief.aspx?q=%e4%bd%9c%e8%80%85%3a(g+farid)&dbcode=ssjd&type=dbpub http://scholar.cnki.net/webpress/brief.aspx?q=%e4%bd%9c%e8%80%85%3a(g+farid)&dbcode=ssjd&type=dbpub NOUN cet-3919 17 46 http://scholar.cnki.net/webpress/brief.aspx?q=%e4%bd%9c%e8%80%85%3a(cristinel+mortici)&dbcode=stjd&type=dbpub http://scholar.cnki.net/webpress/brief.aspx?q=%e4%bd%9c%e8%80%85%3a(cristinel+mortici)&dbcode=stjd&type=dbpub NOUN cet-3919 17 47 following follow VERB cet-3919 17 48 section section NOUN cet-3919 17 49 is be AUX cet-3919 17 50 to to PART cet-3919 17 51 prove prove VERB cet-3919 17 52 the the DET cet-3919 17 53 conclusion conclusion NOUN cet-3919 17 54 of of ADP cet-3919 17 55 lagrange lagrange PROPN cet-3919 17 56 mean mean NOUN cet-3919 17 57 value value NOUN cet-3919 17 58 theorem theorem VERB cet-3919 17 59 : : PUNCT cet-3919 17 60 there there PRON cet-3919 17 61 is be VERB cet-3919 17 62 at at ADV cet-3919 17 63 least least ADV cet-3919 17 64 one one NUM cet-3919 17 65 point point NOUN cet-3919 17 66 f(b)(ab f(b)(ab NOUN cet-3919 17 67 ) ) PUNCT cet-3919 17 68 inside inside ADV cet-3919 17 69 ( ( PUNCT cet-3919 17 70 a a DET cet-3919 17 71 , , PUNCT cet-3919 17 72 b b NOUN cet-3919 17 73 ) ) PUNCT cet-3919 17 74 . . PUNCT cet-3919 18 1 in in ADP cet-3919 18 2 the the DET cet-3919 18 3 process process NOUN cet-3919 18 4 of of ADP cet-3919 18 5 making make VERB cet-3919 18 6 the the DET cet-3919 18 7 equation equation NOUN cet-3919 18 8 ) ) PUNCT cet-3919 18 9 ) ) PUNCT cet-3919 18 10 ( ( PUNCT cet-3919 18 11 ( ( PUNCT cet-3919 18 12 ) ) PUNCT cet-3919 18 13 ( ( PUNCT cet-3919 18 14 ) ) PUNCT cet-3919 18 15 ( ( PUNCT cet-3919 18 16 ' ' PUNCT cet-3919 18 17 abfafbf abfafbf ADJ cet-3919 18 18   PROPN cet-3919 18 19   NOUN cet-3919 18 20 ( ( PUNCT cet-3919 18 21 1 1 NUM cet-3919 18 22 ) ) PUNCT cet-3919 18 23 established establish VERB cet-3919 18 24 , , PUNCT cet-3919 18 25 starting start VERB cet-3919 18 26 from from ADP cet-3919 18 27 the the DET cet-3919 18 28 conclusion conclusion NOUN cet-3919 18 29 f(b)-f(a)=f’()(b f(b)-f(a)=f’()(b ADJ cet-3919 18 30 - - PUNCT cet-3919 18 31 a a NOUN cet-3919 18 32 ) ) PUNCT cet-3919 18 33 , , PUNCT cet-3919 18 34 through through ADP cet-3919 18 35 the the DET cet-3919 18 36 analysis analysis NOUN cet-3919 18 37 of of ADP cet-3919 18 38 this this DET cet-3919 18 39 equation equation NOUN cet-3919 18 40 , , PUNCT cet-3919 18 41 the the DET cet-3919 18 42 auxiliary auxiliary ADJ cet-3919 18 43 function function NOUN cet-3919 18 44 is be AUX cet-3919 18 45 constructed construct VERB cet-3919 18 46 , , PUNCT cet-3919 18 47 and and CCONJ cet-3919 18 48 the the DET cet-3919 18 49 condition condition NOUN cet-3919 18 50 that that SCONJ cet-3919 18 51 the the DET cet-3919 18 52 function function NOUN cet-3919 18 53 f(x f(x PROPN cet-3919 18 54 ) ) PUNCT cet-3919 18 55 satisfies satisfie NOUN cet-3919 18 56 in in ADP cet-3919 18 57 the the DET cet-3919 18 58 theorem theorem NOUN cet-3919 18 59 is be AUX cet-3919 18 60 used use VERB cet-3919 18 61 to to PART cet-3919 18 62 prove prove VERB cet-3919 18 63 the the DET cet-3919 18 64 lagrange lagrange PROPN cet-3919 18 65 mean mean NOUN cet-3919 18 66 value value NOUN cet-3919 18 67 theorem theorem VERB cet-3919 18 68 by by ADP cet-3919 18 69 rolle rolle PROPN cet-3919 18 70 theorem theorem PROPN cet-3919 18 71 . . PUNCT cet-3919 19 1 ( ( PUNCT cet-3919 19 2 2 2 NUM cet-3919 19 3 ) ) PUNCT cet-3919 19 4 to to PART cet-3919 19 5 develop develop VERB cet-3919 19 6 students student NOUN cet-3919 19 7 ’ ' PUNCT cet-3919 19 8 ability ability NOUN cet-3919 19 9 to to PART cet-3919 19 10 use use VERB cet-3919 19 11 the the DET cet-3919 19 12 construction construction NOUN cet-3919 19 13 of of ADP cet-3919 19 14 auxiliary auxiliary ADJ cet-3919 19 15 function function NOUN cet-3919 19 16 to to PART cet-3919 19 17 prove prove VERB cet-3919 19 18 the the DET cet-3919 19 19 mathematical mathematical ADJ cet-3919 19 20 proposition proposition NOUN cet-3919 19 21 while while SCONJ cet-3919 19 22 proving prove VERB cet-3919 19 23 lagrange lagrange NOUN cet-3919 19 24 mean mean NOUN cet-3919 19 25 value value NOUN cet-3919 19 26 theorem theorem NOUN cet-3919 19 27 ( ( PUNCT cet-3919 19 28 heydari heydari NOUN cet-3919 19 29 , , PUNCT cet-3919 19 30 2013 2013 NUM cet-3919 19 31 ) ) PUNCT cet-3919 19 32 , , PUNCT cet-3919 19 33 ( ( PUNCT cet-3919 19 34 tan tan PROPN cet-3919 19 35 , , PUNCT cet-3919 19 36 2014 2014 NUM cet-3919 19 37 ) ) PUNCT cet-3919 19 38 a a DET cet-3919 19 39 relation relation NOUN cet-3919 19 40 between between ADP cet-3919 19 41 the the DET cet-3919 19 42 lagrange lagrange PROPN cet-3919 19 43 mean mean NOUN cet-3919 19 44 value value NOUN cet-3919 19 45 theorem theorem NOUN cet-3919 19 46 and and CCONJ cet-3919 19 47 rolle rolle NOUN cet-3919 19 48 's 's PART cet-3919 19 49 theorem theorem NOUN cet-3919 19 50 is be AUX cet-3919 19 51 found find VERB cet-3919 19 52 from from ADP cet-3919 19 53 the the DET cet-3919 19 54 geometric geometric ADJ cet-3919 19 55 meaning meaning NOUN cet-3919 19 56 . . PUNCT cet-3919 20 1 in in ADP cet-3919 20 2 order order NOUN cet-3919 20 3 to to PART cet-3919 20 4 prove prove VERB cet-3919 20 5 the the DET cet-3919 20 6 lagrange lagrange NOUN cet-3919 20 7 mean mean NOUN cet-3919 20 8 value value NOUN cet-3919 20 9 theorem theorem VERB cet-3919 20 10 with with ADP cet-3919 20 11 the the DET cet-3919 20 12 rolle rolle NOUN cet-3919 20 13 theorem theorem PROPN cet-3919 20 14 , , PUNCT cet-3919 20 15 starting start VERB cet-3919 20 16 from from ADP cet-3919 20 17 the the DET cet-3919 20 18 equation equation NOUN cet-3919 20 19 f(b)-f(a)=f’()(b f(b)-f(a)=f’()(b NOUN cet-3919 20 20 - - PUNCT cet-3919 20 21 a a NOUN cet-3919 20 22 ) ) PUNCT cet-3919 20 23 itself itself PRON cet-3919 20 24 ， ， ADJ cet-3919 20 25 through through ADP cet-3919 20 26 deformation deformation NOUN cet-3919 20 27 of of ADP cet-3919 20 28 the the DET cet-3919 20 29 equation equation NOUN cet-3919 20 30 , , PUNCT cet-3919 20 31 and and CCONJ cet-3919 20 32 by by ADP cet-3919 20 33 making make VERB cet-3919 20 34 use use NOUN cet-3919 20 35 of of ADP cet-3919 20 36 the the DET cet-3919 20 37 property property NOUN cet-3919 20 38 of of ADP cet-3919 20 39 the the DET cet-3919 20 40 function function NOUN cet-3919 20 41 and and CCONJ cet-3919 20 42 the the DET cet-3919 20 43 derivative derivative ADJ cet-3919 20 44 function function NOUN cet-3919 20 45 , , PUNCT cet-3919 20 46 the the DET cet-3919 20 47 auxiliary auxiliary ADJ cet-3919 20 48 function function NOUN cet-3919 20 49 x x X cet-3919 20 50 ab ab PROPN cet-3919 20 51 afbf afbf ADJ cet-3919 20 52 xfxf xfxf PROPN cet-3919 20 53   PROPN cet-3919 20 54   PROPN cet-3919 20 55   PROPN cet-3919 20 56 ) ) PUNCT cet-3919 20 57 ( ( PUNCT cet-3919 20 58 ) ) PUNCT cet-3919 20 59 ( ( PUNCT cet-3919 20 60 ) ) PUNCT cet-3919 20 61 ( ( PUNCT cet-3919 20 62 ) ) PUNCT cet-3919 20 63 ( ( PUNCT cet-3919 20 64 ( ( PUNCT cet-3919 20 65 2 2 X cet-3919 20 66 ) ) PUNCT cet-3919 20 67 as as ADP cet-3919 20 68 the the DET cet-3919 20 69 auxiliary auxiliary ADJ cet-3919 20 70 function function NOUN cet-3919 20 71 f(x f(x PROPN cet-3919 20 72 ) ) PUNCT cet-3919 20 73 satisfies satisfy VERB cet-3919 20 74 the the DET cet-3919 20 75 condition condition NOUN cet-3919 20 76 of of ADP cet-3919 20 77 rolle rolle PROPN cet-3919 20 78 's 's PART cet-3919 20 79 theorem theorem NOUN cet-3919 20 80 , , PUNCT cet-3919 20 81 we we PRON cet-3919 20 82 prove prove VERB cet-3919 20 83 the the DET cet-3919 20 84 lagrange lagrange PROPN cet-3919 20 85 mean mean NOUN cet-3919 20 86 value value NOUN cet-3919 20 87 theorem theorem VERB cet-3919 20 88 by by ADP cet-3919 20 89 using use VERB cet-3919 20 90 the the DET cet-3919 20 91 rolle rolle NOUN cet-3919 20 92 theorem theorem PROPN cet-3919 20 93 ( ( PUNCT cet-3919 20 94 korobkov korobkov NOUN cet-3919 20 95 , , PUNCT cet-3919 20 96 2001 2001 NUM cet-3919 20 97 ) ) PUNCT cet-3919 20 98 , , PUNCT cet-3919 20 99 ( ( PUNCT cet-3919 20 100 elbrous elbrous ADJ cet-3919 20 101 , , PUNCT cet-3919 20 102 2008 2008 NUM cet-3919 20 103 ) ) PUNCT cet-3919 20 104 in in ADP cet-3919 20 105 this this DET cet-3919 20 106 process process NOUN cet-3919 20 107 , , PUNCT cet-3919 20 108 students student NOUN cet-3919 20 109 are be AUX cet-3919 20 110 taught teach VERB cet-3919 20 111 to to PART cet-3919 20 112 prove prove VERB cet-3919 20 113 the the DET cet-3919 20 114 mathematical mathematical ADJ cet-3919 20 115 proposition proposition NOUN cet-3919 20 116 with with ADP cet-3919 20 117 auxiliary auxiliary ADJ cet-3919 20 118 function function NOUN cet-3919 20 119 . . PUNCT cet-3919 21 1 ( ( PUNCT cet-3919 21 2 3 3 X cet-3919 21 3 ) ) PUNCT cet-3919 21 4 to to PART cet-3919 21 5 cultivate cultivate VERB cet-3919 21 6 students student NOUN cet-3919 21 7 ' ' PART cet-3919 21 8 creative creative ADJ cet-3919 21 9 thinking thinking NOUN cet-3919 21 10 ability ability NOUN cet-3919 21 11 . . PUNCT cet-3919 22 1 the the DET cet-3919 22 2 college college NOUN cet-3919 22 3 mathematics mathematic NOUN cet-3919 22 4 teaching teaching NOUN cet-3919 22 5 should should AUX cet-3919 22 6 not not PART cet-3919 22 7 only only ADV cet-3919 22 8 let let VERB cet-3919 22 9 the the DET cet-3919 22 10 students student NOUN cet-3919 22 11 know know VERB cet-3919 22 12 the the DET cet-3919 22 13 existing exist VERB cet-3919 22 14 research research NOUN cet-3919 22 15 methods method NOUN cet-3919 22 16 and and CCONJ cet-3919 22 17 conclusions conclusion NOUN cet-3919 22 18 , , PUNCT cet-3919 22 19 but but CCONJ cet-3919 22 20 also also ADV cet-3919 22 21 need need VERB cet-3919 22 22 to to PART cet-3919 22 23 cultivate cultivate VERB cet-3919 22 24 students student NOUN cet-3919 22 25 ' ' PART cet-3919 22 26 ability ability NOUN cet-3919 22 27 to to PART cet-3919 22 28 discover discover VERB cet-3919 22 29 , , PUNCT cet-3919 22 30 think think VERB cet-3919 22 31 about about ADP cet-3919 22 32 and and CCONJ cet-3919 22 33 solve solve VERB cet-3919 22 34 new new ADJ cet-3919 22 35 problems problem NOUN cet-3919 22 36 . . PUNCT cet-3919 23 1 in in ADP cet-3919 23 2 the the DET cet-3919 23 3 course course NOUN cet-3919 23 4 of of ADP cet-3919 23 5 teaching teaching NOUN cet-3919 23 6 , , PUNCT cet-3919 23 7 i i PRON cet-3919 23 8 should should AUX cet-3919 23 9 take take VERB cet-3919 23 10 the the DET cet-3919 23 11 following follow VERB cet-3919 23 12 innovative innovative ADJ cet-3919 23 13 try try NOUN cet-3919 23 14 : : PUNCT cet-3919 23 15 in in ADP cet-3919 23 16 the the DET cet-3919 23 17 process process NOUN cet-3919 23 18 of of ADP cet-3919 23 19 proving prove VERB cet-3919 23 20 the the DET cet-3919 23 21 lagrange lagrange NOUN cet-3919 23 22 mean mean NOUN cet-3919 23 23 value value NOUN cet-3919 23 24 theorem theorem VERB cet-3919 23 25 , , PUNCT cet-3919 23 26 because because SCONJ cet-3919 23 27 the the DET cet-3919 23 28 function function NOUN cet-3919 23 29 f(x f(x PROPN cet-3919 23 30 ) ) PUNCT cet-3919 23 31 does do AUX cet-3919 23 32 not not PART cet-3919 23 33 satisfy satisfy VERB cet-3919 23 34 the the DET cet-3919 23 35 condition condition NOUN cet-3919 23 36 of of ADP cet-3919 23 37 rolle rolle PROPN cet-3919 23 38 theorem theorem PROPN cet-3919 23 39 , , PUNCT cet-3919 23 40 i i PRON cet-3919 23 41 will will AUX cet-3919 23 42 start start VERB cet-3919 23 43 with with ADP cet-3919 23 44 the the DET cet-3919 23 45 conclusion conclusion NOUN cet-3919 23 46 of of ADP cet-3919 23 47 the the DET cet-3919 23 48 lagrange lagrange PROPN cet-3919 23 49 mean mean NOUN cet-3919 23 50 value value NOUN cet-3919 23 51 theorem theorem VERB cet-3919 23 52 , , PUNCT cet-3919 23 53 and and CCONJ cet-3919 23 54 guide guide VERB cet-3919 23 55 the the DET cet-3919 23 56 students student NOUN cet-3919 23 57 to to PART cet-3919 23 58 analyze analyze VERB cet-3919 23 59 the the DET cet-3919 23 60 equation equation NOUN cet-3919 23 61 f(b)-f(a)=f’()(b f(b)-f(a)=f’()(b NOUN cet-3919 23 62 - - PUNCT cet-3919 23 63 a a NOUN cet-3919 23 64 ) ) PUNCT cet-3919 23 65 with with ADP cet-3919 23 66 the the DET cet-3919 23 67 help help NOUN cet-3919 23 68 of of ADP cet-3919 23 69 the the DET cet-3919 23 70 nature nature NOUN cet-3919 23 71 of of ADP cet-3919 23 72 the the DET cet-3919 23 73 function function NOUN cet-3919 23 74 and and CCONJ cet-3919 23 75 the the DET cet-3919 23 76 derivative derivative ADJ cet-3919 23 77 function function NOUN cet-3919 23 78 , , PUNCT cet-3919 23 79 the the DET cet-3919 23 80 auxiliary auxiliary ADJ cet-3919 23 81 function function NOUN cet-3919 23 82 f(x)= f(x)= ADP cet-3919 23 83 f(x)-((f(b)-f(a))/(b f(x)-((f(b)-f(a))/(b NOUN cet-3919 23 84 - - PUNCT cet-3919 23 85 a a NOUN cet-3919 23 86 ) ) PUNCT cet-3919 23 87 ) ) PUNCT cet-3919 23 88 is be AUX cet-3919 23 89 structured structure VERB cet-3919 23 90 , , PUNCT cet-3919 23 91 and and CCONJ cet-3919 23 92 lagrange lagrange NOUN cet-3919 23 93 mean mean NOUN cet-3919 23 94 value value NOUN cet-3919 23 95 theorem theorem NOUN cet-3919 23 96 is be AUX cet-3919 23 97 proved prove VERB cet-3919 23 98 by by ADP cet-3919 23 99 rolle rolle PROPN cet-3919 23 100 theorem theorem PROPN cet-3919 23 101 . . PUNCT cet-3919 24 1 the the DET cet-3919 24 2 teaching teaching NOUN cet-3919 24 3 material material NOUN cet-3919 24 4 starts start VERB cet-3919 24 5 from from ADP cet-3919 24 6 the the DET cet-3919 24 7 geometric geometric ADJ cet-3919 24 8 meaning meaning NOUN cet-3919 24 9 of of ADP cet-3919 24 10 the the DET cet-3919 24 11 lagrange lagrange NOUN cet-3919 24 12 mean mean NOUN cet-3919 24 13 value value NOUN cet-3919 24 14 theorem theorem VERB cet-3919 24 15 , , PUNCT cet-3919 24 16 combined combine VERB cet-3919 24 17 with with ADP cet-3919 24 18 the the DET cet-3919 24 19 graphics graphic NOUN cet-3919 24 20 figure figure NOUN cet-3919 24 21 1 1 NUM cet-3919 24 22 : : PUNCT cet-3919 24 23 geometric geometric ADJ cet-3919 24 24 sketch sketch NOUN cet-3919 24 25 of of ADP cet-3919 24 26 lagrange lagrange PROPN cet-3919 24 27 mean mean NOUN cet-3919 24 28 value value NOUN cet-3919 24 29 theorem theorem VERB cet-3919 24 30 the the DET cet-3919 24 31 auxiliary auxiliary ADJ cet-3919 24 32 function function NOUN cet-3919 24 33 ) ) PUNCT cet-3919 24 34 ] ] PUNCT cet-3919 24 35 ( ( PUNCT cet-3919 24 36 ) ) PUNCT cet-3919 24 37 ( ( PUNCT cet-3919 24 38 ) ) PUNCT cet-3919 24 39 ( ( PUNCT cet-3919 24 40 ) ) PUNCT cet-3919 24 41 ( ( PUNCT cet-3919 24 42 [ [ NOUN cet-3919 24 43 ) ) PUNCT cet-3919 24 44 ( ( PUNCT cet-3919 24 45 ) ) PUNCT cet-3919 24 46 ( ( PUNCT cet-3919 24 47 ax ax NOUN cet-3919 24 48 ab ab PROPN cet-3919 24 49 afbf afbf ADJ cet-3919 24 50 afxfxf afxfxf PROPN cet-3919 24 51   PROPN cet-3919 24 52   PROPN cet-3919 24 53   PROPN cet-3919 24 54   NUM cet-3919 24 55 ( ( PUNCT cet-3919 24 56 3 3 X cet-3919 24 57 ) ) PUNCT cet-3919 24 58 is be AUX cet-3919 24 59 constructed construct VERB cet-3919 24 60 by by ADP cet-3919 24 61 analyzing analyze VERB cet-3919 24 62 the the DET cet-3919 24 63 characteristic characteristic NOUN cet-3919 24 64 of of ADP cet-3919 24 65 the the DET cet-3919 24 66 length length NOUN cet-3919 24 67 function function NOUN cet-3919 24 68 of of ADP cet-3919 24 69 the the DET cet-3919 24 70 line line NOUN cet-3919 24 71 segment segment NOUN cet-3919 24 72 nm nm PROPN cet-3919 24 73 . . PUNCT cet-3919 25 1 similarly similarly ADV cet-3919 25 2 , , PUNCT cet-3919 25 3 to to ADP cet-3919 25 4 the the DET cet-3919 25 5 function function NOUN cet-3919 25 6 f(x f(x PROPN cet-3919 25 7 ) ) PUNCT cet-3919 25 8 , , PUNCT cet-3919 25 9 the the DET cet-3919 25 10 lagrange lagrange NOUN cet-3919 25 11 mean mean NOUN cet-3919 25 12 value value NOUN cet-3919 25 13 theorem theorem NOUN cet-3919 25 14 is be AUX cet-3919 25 15 proved prove VERB cet-3919 25 16 by by ADP cet-3919 25 17 the the DET cet-3919 25 18 rolle rolle NOUN cet-3919 25 19 theorem theorem PROPN cet-3919 25 20 ( ( PUNCT cet-3919 25 21 tong tong PROPN cet-3919 25 22 , , PUNCT cet-3919 25 23 2000 2000 NUM cet-3919 25 24 ) ) PUNCT cet-3919 25 25 . . PUNCT cet-3919 26 1 in in ADP cet-3919 26 2 the the DET cet-3919 26 3 process process NOUN cet-3919 26 4 , , PUNCT cet-3919 26 5 i i PRON cet-3919 26 6 guide guide VERB cet-3919 26 7 the the DET cet-3919 26 8 students student NOUN cet-3919 26 9 to to PART cet-3919 26 10 compare compare VERB cet-3919 26 11 the the DET cet-3919 26 12 two two NUM cet-3919 26 13 kinds kind NOUN cet-3919 26 14 of of ADP cet-3919 26 15 auxiliary auxiliary ADJ cet-3919 26 16 functions function NOUN cet-3919 26 17 and and CCONJ cet-3919 26 18 detect detect VERB cet-3919 26 19 the the DET cet-3919 26 20 characteristics characteristic NOUN cet-3919 26 21 and and CCONJ cet-3919 26 22 the the DET cet-3919 26 23 differences difference NOUN cet-3919 26 24 between between ADP cet-3919 26 25 them they PRON cet-3919 26 26 ( ( PUNCT cet-3919 26 27 zabrdjko zabrdjko PROPN cet-3919 26 28 , , PUNCT cet-3919 26 29 1996 1996 NUM cet-3919 26 30 ) ) PUNCT cet-3919 26 31 , , PUNCT cet-3919 26 32 and and CCONJ cet-3919 26 33 analyze analyze VERB cet-3919 26 34 the the DET cet-3919 26 35 constructing construct VERB cet-3919 26 36 context context NOUN cet-3919 26 37 and and CCONJ cet-3919 26 38 perspective perspective NOUN cet-3919 26 39 of of ADP cet-3919 26 40 the the DET cet-3919 26 41 two two NUM cet-3919 26 42 auxiliary auxiliary ADJ cet-3919 26 43 functions function NOUN cet-3919 26 44 . . PUNCT cet-3919 27 1 by by ADP cet-3919 27 2 contrast contrast NOUN cet-3919 27 3 , , PUNCT cet-3919 27 4 make make VERB cet-3919 27 5 the the DET cet-3919 27 6 students student NOUN cet-3919 27 7 experience experience VERB cet-3919 27 8 different different ADJ cet-3919 27 9 ( ( PUNCT cet-3919 27 10 lupu lupu PROPN cet-3919 27 11 , , PUNCT cet-3919 27 12 2009 2009 NUM cet-3919 27 13 ) ) PUNCT cet-3919 27 14 , , PUNCT cet-3919 27 15 multi multi ADJ cet-3919 27 16 - - ADJ cet-3919 27 17 angle angle ADJ cet-3919 27 18 method method NOUN cet-3919 27 19 of of ADP cet-3919 27 20 constructing construct VERB cet-3919 27 21 auxiliary auxiliary ADJ cet-3919 27 22 function function NOUN cet-3919 27 23 . . PUNCT cet-3919 28 1 meanwhile meanwhile ADV cet-3919 28 2 , , PUNCT cet-3919 28 3 by by ADP cet-3919 28 4 inspiring inspire VERB cet-3919 28 5 students student NOUN cet-3919 28 6 to to PART cet-3919 28 7 think think VERB cet-3919 28 8 whether whether SCONJ cet-3919 28 9 different different ADJ cet-3919 28 10 auxiliary auxiliary ADJ cet-3919 28 11 functions function NOUN cet-3919 28 12 can can AUX cet-3919 28 13 be be AUX cet-3919 28 14 constructed construct VERB cet-3919 28 15 to to PART cet-3919 28 16 prove prove VERB cet-3919 28 17 theorems theorem NOUN cet-3919 28 18 , , PUNCT cet-3919 28 19 i i PRON cet-3919 28 20 guide guide VERB cet-3919 28 21 the the DET cet-3919 28 22 students student NOUN cet-3919 28 23 to to PART cet-3919 28 24 find find VERB cet-3919 28 25 the the DET cet-3919 28 26 problem problem NOUN cet-3919 28 27 , , PUNCT cet-3919 28 28 propose propose VERB cet-3919 28 29 the the DET cet-3919 28 30 question question NOUN cet-3919 28 31 , , PUNCT cet-3919 28 32 analyze analyze NOUN cet-3919 28 33 question question NOUN cet-3919 28 34 , , PUNCT cet-3919 28 35 and and CCONJ cet-3919 28 36 solve solve VERB cet-3919 28 37 the the DET cet-3919 28 38 problem problem NOUN cet-3919 28 39 , , PUNCT cet-3919 28 40 cultivating cultivate VERB cet-3919 28 41 students student NOUN cet-3919 28 42 ’ ' PUNCT cet-3919 28 43 awareness awareness NOUN cet-3919 28 44 of of ADP cet-3919 28 45 innovation innovation NOUN cet-3919 28 46 and and CCONJ cet-3919 28 47 innovative innovative ADJ cet-3919 28 48 thinking thinking NOUN cet-3919 28 49 ability ability NOUN cet-3919 28 50 . . PUNCT cet-3919 29 1 326 326 NUM cet-3919 29 2 http://fanyi.baidu.com/#auto/auto/develop http://fanyi.baidu.com/#auto/auto/develop ADJ cet-3919 29 3 http://scholar.cnki.net/webpress/brief.aspx?q=%e4%bd%9c%e8%80%85%3a(m.+heydari)&dbcode=sjes&type=dbpub http://scholar.cnki.net/webpress/brief.aspx?q=%e4%bd%9c%e8%80%85%3a(m.+heydari)&dbcode=sjes&type=dbpub PROPN cet-3919 29 4 http://scholar.cnki.net/webpress/brief.aspx?q=%e4%bd%9c%e8%80%85%3a(cezar+lupu)&dbcode=sjdj&type=dbpub http://scholar.cnki.net/webpress/brief.aspx?q=%e4%bd%9c%e8%80%85%3a(cezar+lupu)&dbcode=sjdj&type=dbpub NOUN cet-3919 29 5 ( ( PUNCT cet-3919 29 6 4 4 NUM cet-3919 29 7 ) ) PUNCT cet-3919 29 8 to to PART cet-3919 29 9 cultivate cultivate VERB cet-3919 29 10 students student NOUN cet-3919 29 11 ’ ' PUNCT cet-3919 29 12 ability ability NOUN cet-3919 29 13 of of ADP cet-3919 29 14 comprehensive comprehensive ADJ cet-3919 29 15 analysis analysis NOUN cet-3919 29 16 of of ADP cet-3919 29 17 the the DET cet-3919 29 18 problem problem NOUN cet-3919 29 19 and and CCONJ cet-3919 29 20 the the DET cet-3919 29 21 comprehensive comprehensive ADJ cet-3919 29 22 use use NOUN cet-3919 29 23 of of ADP cet-3919 29 24 through through ADP cet-3919 29 25 the the DET cet-3919 29 26 proof proof NOUN cet-3919 29 27 of of ADP cet-3919 29 28 the the DET cet-3919 29 29 theorem theorem NOUN cet-3919 29 30 and and CCONJ cet-3919 29 31 the the DET cet-3919 29 32 proof proof NOUN cet-3919 29 33 of of ADP cet-3919 29 34 two two NUM cet-3919 29 35 examples example NOUN cet-3919 29 36 on on ADP cet-3919 29 37 the the DET cet-3919 29 38 equality equality NOUN cet-3919 29 39 and and CCONJ cet-3919 29 40 inequality inequality NOUN cet-3919 29 41 by by ADP cet-3919 29 42 the the DET cet-3919 29 43 theorem theorem ADJ cet-3919 29 44 , , PUNCT cet-3919 29 45 knowledge knowledge NOUN cet-3919 29 46 , , PUNCT cet-3919 29 47 and and CCONJ cet-3919 29 48 with with ADP cet-3919 29 49 the the DET cet-3919 29 50 help help NOUN cet-3919 29 51 of of ADP cet-3919 29 52 the the DET cet-3919 29 53 assignments assignment NOUN cet-3919 29 54 , , PUNCT cet-3919 29 55 the the DET cet-3919 29 56 students student NOUN cet-3919 29 57 are be AUX cet-3919 29 58 supposed suppose VERB cet-3919 29 59 to to PART cet-3919 29 60 grasp grasp VERB cet-3919 29 61 the the DET cet-3919 29 62 following follow VERB cet-3919 29 63 two two NUM cet-3919 29 64 kinds kind NOUN cet-3919 29 65 of of ADP cet-3919 29 66 abilities ability NOUN cet-3919 29 67 of of ADP cet-3919 29 68 analyzing analyze VERB cet-3919 29 69 problems problem NOUN cet-3919 29 70 and and CCONJ cet-3919 29 71 the the DET cet-3919 29 72 comprehensive comprehensive ADJ cet-3919 29 73 use use NOUN cet-3919 29 74 of of ADP cet-3919 29 75 knowledge knowledge NOUN cet-3919 29 76 . . PUNCT cet-3919 30 1 2.3 2.3 NUM cet-3919 30 2 teaching teaching NOUN cet-3919 30 3 focus focus NOUN cet-3919 30 4 and and CCONJ cet-3919 30 5 difficulty difficulty NOUN cet-3919 30 6 teaching teach VERB cet-3919 30 7 focus focus NOUN cet-3919 30 8 : : PUNCT cet-3919 30 9 lagrange lagrange NOUN cet-3919 30 10 mean mean NOUN cet-3919 30 11 value value NOUN cet-3919 30 12 theorem theorem VERB cet-3919 30 13 teaching teaching NOUN cet-3919 30 14 difficulty difficulty NOUN cet-3919 30 15 : : PUNCT cet-3919 30 16 the the DET cet-3919 30 17 construction construction NOUN cet-3919 30 18 of of ADP cet-3919 30 19 auxiliary auxiliary ADJ cet-3919 30 20 function function NOUN cet-3919 30 21 , , PUNCT cet-3919 30 22 the the DET cet-3919 30 23 application application NOUN cet-3919 30 24 of of ADP cet-3919 30 25 lagrange lagrange PROPN cet-3919 30 26 mean mean NOUN cet-3919 30 27 value value NOUN cet-3919 30 28 theorem theorem VERB cet-3919 30 29 2.4 2.4 NUM cet-3919 30 30 teaching teaching NOUN cet-3919 30 31 strategies strategy NOUN cet-3919 30 32 review review VERB cet-3919 30 33 the the DET cet-3919 30 34 old old ADJ cet-3919 30 35 and and CCONJ cet-3919 30 36 learn learn VERB cet-3919 30 37 the the DET cet-3919 30 38 new new ADJ cet-3919 30 39 , , PUNCT cet-3919 30 40 put put VERB cet-3919 30 41 forward forward ADV cet-3919 30 42 the the DET cet-3919 30 43 question question NOUN cet-3919 30 44 , , PUNCT cet-3919 30 45 introduce introduce VERB cet-3919 30 46 new new ADJ cet-3919 30 47 courses course NOUN cet-3919 30 48 : : PUNCT cet-3919 30 49 looking look VERB cet-3919 30 50 back back ADV cet-3919 30 51 on on ADP cet-3919 30 52 the the DET cet-3919 30 53 learned learn VERB cet-3919 30 54 knowledge knowledge NOUN cet-3919 30 55 : : PUNCT cet-3919 30 56 review review VERB cet-3919 30 57 the the DET cet-3919 30 58 old old ADJ cet-3919 30 59 : : PUNCT cet-3919 30 60 rolle rolle NOUN cet-3919 30 61 theorem theorem VERB cet-3919 30 62 if if SCONJ cet-3919 30 63 the the DET cet-3919 30 64 function function NOUN cet-3919 30 65 f(x f(x PROPN cet-3919 30 66 ) ) PUNCT cet-3919 30 67 is be AUX cet-3919 30 68 satisfied satisfied ADJ cet-3919 30 69 : : PUNCT cet-3919 30 70 ( ( PUNCT cet-3919 30 71 1 1 X cet-3919 30 72 ) ) PUNCT cet-3919 30 73 be be AUX cet-3919 30 74 continuous continuous ADJ cet-3919 30 75 on on ADP cet-3919 30 76 the the DET cet-3919 30 77 closed closed ADJ cet-3919 30 78 interval interval NOUN cet-3919 30 79 [ [ X cet-3919 30 80 a a X cet-3919 30 81 , , PUNCT cet-3919 30 82 b b NOUN cet-3919 30 83 ] ] X cet-3919 30 84 , , PUNCT cet-3919 30 85 ( ( PUNCT cet-3919 30 86 2 2 X cet-3919 30 87 ) ) PUNCT cet-3919 30 88 be be AUX cet-3919 30 89 derivable derivable ADJ cet-3919 30 90 in in ADP cet-3919 30 91 the the DET cet-3919 30 92 open open ADJ cet-3919 30 93 interval interval NOUN cet-3919 30 94 ( ( PUNCT cet-3919 30 95 a a DET cet-3919 30 96 , , PUNCT cet-3919 30 97 b b NOUN cet-3919 30 98 ) ) PUNCT cet-3919 30 99 , , PUNCT cet-3919 30 100 ( ( PUNCT cet-3919 30 101 3 3 X cet-3919 30 102 ) ) PUNCT cet-3919 30 103 be be AUX cet-3919 30 104 equal equal ADJ cet-3919 30 105 to to ADP cet-3919 30 106 the the DET cet-3919 30 107 value value NOUN cet-3919 30 108 of of ADP cet-3919 30 109 the the DET cet-3919 30 110 function function NOUN cet-3919 30 111 at at ADP cet-3919 30 112 the the DET cet-3919 30 113 point point NOUN cet-3919 30 114 of of ADP cet-3919 30 115 the the DET cet-3919 30 116 interval interval NOUN cet-3919 30 117 , , PUNCT cet-3919 30 118 that that PRON cet-3919 30 119 is is ADV cet-3919 30 120 f(a)=f(b).then f(a)=f(b).then NOUN cet-3919 30 121 there there PRON cet-3919 30 122 is be VERB cet-3919 30 123 at at ADV cet-3919 30 124 least least ADJ cet-3919 30 125 one one NUM cet-3919 30 126 point point NOUN cet-3919 30 127 (ab (ab NOUN cet-3919 30 128 ) ) PUNCT cet-3919 30 129 , , PUNCT cet-3919 30 130 in in ADP cet-3919 30 131 the the DET cet-3919 30 132 interior interior NOUN cet-3919 30 133 ( ( PUNCT cet-3919 30 134 a a DET cet-3919 30 135 , , PUNCT cet-3919 30 136 b b NOUN cet-3919 30 137 ) ) PUNCT cet-3919 30 138 so so SCONJ cet-3919 30 139 that that SCONJ cet-3919 30 140 the the DET cet-3919 30 141 derivative derivative NOUN cet-3919 30 142 of of ADP cet-3919 30 143 the the DET cet-3919 30 144 function function NOUN cet-3919 30 145 f(x f(x PROPN cet-3919 30 146 ) ) PUNCT cet-3919 30 147 at at ADP cet-3919 30 148 that that DET cet-3919 30 149 point point NOUN cet-3919 30 150 is be AUX cet-3919 30 151 equal equal ADJ cet-3919 30 152 to to ADP cet-3919 30 153 zero zero NUM cet-3919 30 154 , , PUNCT cet-3919 30 155 that that PRON cet-3919 30 156 is be AUX cet-3919 30 157 f’()=0 f’()=0 ADJ cet-3919 30 158 ask ask VERB cet-3919 30 159 the the DET cet-3919 30 160 question question NOUN cet-3919 30 161 : : PUNCT cet-3919 30 162 if if SCONJ cet-3919 30 163 the the DET cet-3919 30 164 third third ADJ cet-3919 30 165 condition condition NOUN cet-3919 30 166 of of ADP cet-3919 30 167 rolle rolle PROPN cet-3919 30 168 's 's PART cet-3919 30 169 theorem theorem NOUN cet-3919 30 170 is be AUX cet-3919 30 171 moved move VERB cet-3919 30 172 , , PUNCT cet-3919 30 173 what what DET cet-3919 30 174 conclusion conclusion NOUN cet-3919 30 175 can can AUX cet-3919 30 176 we we PRON cet-3919 30 177 get get VERB cet-3919 30 178 ( ( PUNCT cet-3919 30 179 comparative comparative ADJ cet-3919 30 180 inspiration inspiration NOUN cet-3919 30 181 , , PUNCT cet-3919 30 182 to to PART cet-3919 30 183 be be AUX cet-3919 30 184 discussed discuss VERB cet-3919 30 185 ) ) PUNCT cet-3919 30 186 introduce introduce VERB cet-3919 30 187 new new ADJ cet-3919 30 188 courses course NOUN cet-3919 30 189 : : PUNCT cet-3919 30 190 lagrange lagrange NOUN cet-3919 30 191 mean mean NOUN cet-3919 30 192 value value NOUN cet-3919 30 193 theorem theorem NOUN cet-3919 30 194 and and CCONJ cet-3919 30 195 its its PRON cet-3919 30 196 application application NOUN cet-3919 30 197 heuristic heuristic ADJ cet-3919 30 198 induction induction NOUN cet-3919 30 199 , , PUNCT cet-3919 30 200 theorem theorem ADJ cet-3919 30 201 proving proving NOUN cet-3919 30 202 : : PUNCT cet-3919 30 203 in in ADP cet-3919 30 204 each each DET cet-3919 30 205 step step NOUN cet-3919 30 206 of of ADP cet-3919 30 207 the the DET cet-3919 30 208 class class NOUN cet-3919 30 209 , , PUNCT cet-3919 30 210 including include VERB cet-3919 30 211 the the DET cet-3919 30 212 discussion discussion NOUN cet-3919 30 213 of of ADP cet-3919 30 214 the the DET cet-3919 30 215 geometric geometric ADJ cet-3919 30 216 significance significance NOUN cet-3919 30 217 of of ADP cet-3919 30 218 theorem theorem NOUN cet-3919 30 219 , , PUNCT cet-3919 30 220 the the DET cet-3919 30 221 construction construction NOUN cet-3919 30 222 of of ADP cet-3919 30 223 the the DET cet-3919 30 224 auxiliary auxiliary ADJ cet-3919 30 225 function function NOUN cet-3919 30 226 from from ADP cet-3919 30 227 the the DET cet-3919 30 228 analysis analysis NOUN cet-3919 30 229 of of ADP cet-3919 30 230 the the DET cet-3919 30 231 conclusion conclusion NOUN cet-3919 30 232 of of ADP cet-3919 30 233 theorem theorem NOUN cet-3919 30 234 , , PUNCT cet-3919 30 235 the the DET cet-3919 30 236 proof proof NOUN cet-3919 30 237 of of ADP cet-3919 30 238 the the DET cet-3919 30 239 lagrange lagrange PROPN cet-3919 30 240 mean mean NOUN cet-3919 30 241 value value NOUN cet-3919 30 242 theorem theorem VERB cet-3919 30 243 by by ADP cet-3919 30 244 the the DET cet-3919 30 245 rolle rolle NOUN cet-3919 30 246 theorem theorem PROPN cet-3919 30 247 , , PUNCT cet-3919 30 248 the the DET cet-3919 30 249 analysis analysis NOUN cet-3919 30 250 and and CCONJ cet-3919 30 251 proof proof NOUN cet-3919 30 252 of of ADP cet-3919 30 253 the the DET cet-3919 30 254 two two NUM cet-3919 30 255 examples example NOUN cet-3919 30 256 of of ADP cet-3919 30 257 equality equality NOUN cet-3919 30 258 and and CCONJ cet-3919 30 259 inequality inequality NOUN cet-3919 30 260 ( ( PUNCT cet-3919 30 261 liu liu PROPN cet-3919 30 262 , , PUNCT cet-3919 30 263 2015 2015 NUM cet-3919 30 264 ) ) PUNCT cet-3919 30 265 , , PUNCT cet-3919 30 266 i i PRON cet-3919 30 267 duly duly ADV cet-3919 30 268 inspired inspire VERB cet-3919 30 269 and and CCONJ cet-3919 30 270 guided guide VERB cet-3919 30 271 the the DET cet-3919 30 272 students student NOUN cet-3919 30 273 to to PART cet-3919 30 274 think think VERB cet-3919 30 275 actively actively ADV cet-3919 30 276 , , PUNCT cet-3919 30 277 participate participate VERB cet-3919 30 278 in in ADP cet-3919 30 279 the the DET cet-3919 30 280 classroom classroom NOUN cet-3919 30 281 , , PUNCT cet-3919 30 282 and and CCONJ cet-3919 30 283 seek seek VERB cet-3919 30 284 the the DET cet-3919 30 285 functions function NOUN cet-3919 30 286 that that PRON cet-3919 30 287 meet meet VERB cet-3919 30 288 the the DET cet-3919 30 289 conditions condition NOUN cet-3919 30 290 and and CCONJ cet-3919 30 291 the the DET cet-3919 30 292 corresponding corresponding ADJ cet-3919 30 293 interval interval NOUN cet-3919 30 294 , , PUNCT cet-3919 30 295 thereby thereby ADV cet-3919 30 296 successfully successfully ADV cet-3919 30 297 applied apply VERB cet-3919 30 298 theorem theorem ADJ cet-3919 30 299 to to PART cet-3919 30 300 prove prove VERB cet-3919 30 301 the the DET cet-3919 30 302 problems problem NOUN cet-3919 30 303 related relate VERB cet-3919 30 304 . . PUNCT cet-3919 31 1 method method NOUN cet-3919 31 2 training training NOUN cet-3919 31 3 , , PUNCT cet-3919 31 4 migration migration NOUN cet-3919 31 5 and and CCONJ cet-3919 31 6 expansion expansion NOUN cet-3919 31 7 : : PUNCT cet-3919 31 8 teacher teacher NOUN cet-3919 31 9 - - PUNCT cet-3919 31 10 oriented orient VERB cet-3919 31 11 class class NOUN cet-3919 31 12 emphasizes emphasize VERB cet-3919 31 13 the the DET cet-3919 31 14 one one NUM cet-3919 31 15 - - PUNCT cet-3919 31 16 way way NOUN cet-3919 31 17 knowledge knowledge NOUN cet-3919 31 18 transference transference NOUN cet-3919 31 19 of of ADP cet-3919 31 20 the the DET cet-3919 31 21 teacher teacher NOUN cet-3919 31 22 and and CCONJ cet-3919 31 23 the the DET cet-3919 31 24 memorizing memorize VERB cet-3919 31 25 work work NOUN cet-3919 31 26 on on ADP cet-3919 31 27 the the DET cet-3919 31 28 students student NOUN cet-3919 31 29 , , PUNCT cet-3919 31 30 is be AUX cet-3919 31 31 the the DET cet-3919 31 32 teachers teacher NOUN cet-3919 31 33 ’ ' PUNCT cet-3919 31 34 " " PUNCT cet-3919 31 35 autocracy autocracy NOUN cet-3919 31 36 " " PUNCT cet-3919 31 37 , , PUNCT cet-3919 31 38 " " PUNCT cet-3919 31 39 chalk chalk NOUN cet-3919 31 40 and and CCONJ cet-3919 31 41 talk talk NOUN cet-3919 31 42 " " PUNCT cet-3919 31 43 . . PUNCT cet-3919 32 1 while while SCONJ cet-3919 32 2 the the DET cet-3919 32 3 students student NOUN cet-3919 32 4 - - PUNCT cet-3919 32 5 oriented orient VERB cet-3919 32 6 teaching teaching NOUN cet-3919 32 7 reform reform NOUN cet-3919 32 8 attaches attach VERB cet-3919 32 9 importance importance NOUN cet-3919 32 10 to to ADP cet-3919 32 11 comprehensive comprehensive ADJ cet-3919 32 12 assistance assistance NOUN cet-3919 32 13 from from ADP cet-3919 32 14 the the DET cet-3919 32 15 teacher teacher NOUN cet-3919 32 16 to to ADP cet-3919 32 17 the the DET cet-3919 32 18 students student NOUN cet-3919 32 19 and and CCONJ cet-3919 32 20 should should AUX cet-3919 32 21 provide provide VERB cet-3919 32 22 students student NOUN cet-3919 32 23 opportunities opportunity NOUN cet-3919 32 24 for for ADP cet-3919 32 25 autonomous autonomous ADJ cet-3919 32 26 learning learning NOUN cet-3919 32 27 on on ADP cet-3919 32 28 the the DET cet-3919 32 29 students student NOUN cet-3919 32 30 ’ ' PUNCT cet-3919 32 31 part part NOUN cet-3919 32 32 ( ( PUNCT cet-3919 32 33 niu niu PROPN cet-3919 32 34 , , PUNCT cet-3919 32 35 2015 2015 NUM cet-3919 32 36 ) ) PUNCT cet-3919 32 37 , , PUNCT cet-3919 32 38 and and CCONJ cet-3919 32 39 give give VERB cet-3919 32 40 students student NOUN cet-3919 32 41 time time NOUN cet-3919 32 42 and and CCONJ cet-3919 32 43 tasks task NOUN cet-3919 32 44 for for ADP cet-3919 32 45 mental mental ADJ cet-3919 32 46 work work NOUN cet-3919 32 47 in in ADP cet-3919 32 48 order order NOUN cet-3919 32 49 to to PART cet-3919 32 50 facilitate facilitate VERB cet-3919 32 51 students student NOUN cet-3919 32 52 to to PART cet-3919 32 53 master master VERB cet-3919 32 54 the the DET cet-3919 32 55 learning learning NOUN cet-3919 32 56 method method NOUN cet-3919 32 57 and and CCONJ cet-3919 32 58 use use NOUN cet-3919 32 59 of of ADP cet-3919 32 60 migration migration NOUN cet-3919 32 61 in in ADP cet-3919 32 62 the the DET cet-3919 32 63 new new ADJ cet-3919 32 64 situation situation NOUN cet-3919 32 65 . . PUNCT cet-3919 33 1 after after ADP cet-3919 33 2 the the DET cet-3919 33 3 proof proof NOUN cet-3919 33 4 of of ADP cet-3919 33 5 the the DET cet-3919 33 6 problems problem NOUN cet-3919 33 7 of of ADP cet-3919 33 8 the the DET cet-3919 33 9 equality equality NOUN cet-3919 33 10 in in ADP cet-3919 33 11 example example NOUN cet-3919 33 12 1 1 NUM cet-3919 33 13 with with ADP cet-3919 33 14 lagrange lagrange NOUN cet-3919 33 15 mean mean NOUN cet-3919 33 16 value value NOUN cet-3919 33 17 theorem theorem NOUN cet-3919 33 18 ( ( PUNCT cet-3919 33 19 zhu zhu PROPN cet-3919 33 20 , , PUNCT cet-3919 33 21 2015 2015 NUM cet-3919 33 22 ) ) PUNCT cet-3919 33 23 , , PUNCT cet-3919 33 24 the the DET cet-3919 33 25 problem problem NOUN cet-3919 33 26 is be AUX cet-3919 33 27 proposed propose VERB cet-3919 33 28 that that SCONJ cet-3919 33 29 whether whether SCONJ cet-3919 33 30 the the DET cet-3919 33 31 theorem theorem NOUN cet-3919 33 32 also also ADV cet-3919 33 33 has have VERB cet-3919 33 34 application application NOUN cet-3919 33 35 in in ADP cet-3919 33 36 other other ADJ cet-3919 33 37 aspects aspect NOUN cet-3919 33 38 . . PUNCT cet-3919 34 1 the the DET cet-3919 34 2 inequality inequality NOUN cet-3919 34 3 proof proof NOUN cet-3919 34 4 problem problem NOUN cet-3919 34 5 of of ADP cet-3919 34 6 2 2 NUM cet-3919 34 7 is be AUX cet-3919 34 8 drawn draw VERB cet-3919 34 9 off off ADP cet-3919 34 10 . . PUNCT cet-3919 35 1 that that PRON cet-3919 35 2 is be AUX cet-3919 35 3 to to PART cet-3919 35 4 prove prove VERB cet-3919 35 5 when when SCONJ cet-3919 35 6 x0 x0 PROPN cet-3919 35 7 , , PUNCT cet-3919 35 8 xx xx NUM cet-3919 35 9 x x SYM cet-3919 35 10 x x SYM cet-3919 35 11   NOUN cet-3919 35 12   ADJ cet-3919 35 13 ) ) PUNCT cet-3919 35 14 1ln 1ln NOUN cet-3919 35 15 ( ( PUNCT cet-3919 35 16 1 1 NUM cet-3919 35 17 ( ( PUNCT cet-3919 35 18 4 4 NUM cet-3919 35 19 ) ) PUNCT cet-3919 35 20 ( ( PUNCT cet-3919 35 21 this this DET cet-3919 35 22 question question NOUN cet-3919 35 23 has have VERB cet-3919 35 24 a a DET cet-3919 35 25 certain certain ADJ cet-3919 35 26 degree degree NOUN cet-3919 35 27 of of ADP cet-3919 35 28 difficulty difficulty NOUN cet-3919 35 29 , , PUNCT cet-3919 35 30 pay pay VERB cet-3919 35 31 attention attention NOUN cet-3919 35 32 to to ADP cet-3919 35 33 timely timely ADJ cet-3919 35 34 guidance guidance NOUN cet-3919 35 35 ) ) PUNCT cet-3919 35 36 . . PUNCT cet-3919 36 1 2.5 2.5 NUM cet-3919 36 2 methods method NOUN cet-3919 36 3 , , PUNCT cet-3919 36 4 means mean VERB cet-3919 36 5 and and CCONJ cet-3919 36 6 matters matter NOUN cet-3919 36 7 needing need VERB cet-3919 36 8 attention attention NOUN cet-3919 36 9 teaching teaching NOUN cet-3919 36 10 methods method NOUN cet-3919 36 11 : : PUNCT cet-3919 36 12 heuristic heuristic ADJ cet-3919 36 13 teaching teaching NOUN cet-3919 36 14 , , PUNCT cet-3919 36 15 example example NOUN cet-3919 36 16 teaching teaching NOUN cet-3919 36 17 , , PUNCT cet-3919 36 18 analogy analogy NOUN cet-3919 36 19 teaching teaching NOUN cet-3919 36 20 teaching teaching NOUN cet-3919 36 21 means mean VERB cet-3919 36 22 : : PUNCT cet-3919 36 23 the the DET cet-3919 36 24 combination combination NOUN cet-3919 36 25 of of ADP cet-3919 36 26 classroom classroom NOUN cet-3919 36 27 teaching teaching NOUN cet-3919 36 28 and and CCONJ cet-3919 36 29 the the DET cet-3919 36 30 use use NOUN cet-3919 36 31 of of ADP cet-3919 36 32 multimedia multimedia NOUN cet-3919 36 33 courseware courseware NOUN cet-3919 36 34 . . PUNCT cet-3919 37 1 matters matter NOUN cet-3919 37 2 needing need VERB cet-3919 37 3 attention attention NOUN cet-3919 37 4 : : PUNCT cet-3919 37 5 the the DET cet-3919 37 6 similarities similarity NOUN cet-3919 37 7 and and CCONJ cet-3919 37 8 differences difference NOUN cet-3919 37 9 of of ADP cet-3919 37 10 condition condition NOUN cet-3919 37 11 and and CCONJ cet-3919 37 12 conclusion conclusion NOUN cet-3919 37 13 between between ADP cet-3919 37 14 rolle rolle PROPN cet-3919 37 15 's 's PART cet-3919 37 16 theorem theorem PROPN cet-3919 37 17 and and CCONJ cet-3919 37 18 lagrange lagrange PROPN cet-3919 37 19 theorem theorem NOUN cet-3919 37 20 and and CCONJ cet-3919 37 21 the the DET cet-3919 37 22 relationship relationship NOUN cet-3919 37 23 between between ADP cet-3919 37 24 them they PRON cet-3919 37 25 ; ; PUNCT cet-3919 37 26 rolle rolle PROPN cet-3919 37 27 's 's PART cet-3919 37 28 theorem theorem NOUN cet-3919 37 29 is be AUX cet-3919 37 30 a a DET cet-3919 37 31 special special ADJ cet-3919 37 32 case case NOUN cet-3919 37 33 of of ADP cet-3919 37 34 the the DET cet-3919 37 35 lagrangian lagrangian ADJ cet-3919 37 36 theorem theorem NOUN cet-3919 37 37 ; ; PUNCT cet-3919 37 38 lagrange lagrange NOUN cet-3919 37 39 theorem theorem NOUN cet-3919 37 40 is be AUX cet-3919 37 41 generalization generalization NOUN cet-3919 37 42 of of ADP cet-3919 37 43 rolle rolle PROPN cet-3919 37 44 's 's PART cet-3919 37 45 theorem theorem NOUN cet-3919 37 46 ; ; PUNCT cet-3919 37 47 note note VERB cet-3919 37 48 the the DET cet-3919 37 49 mean mean ADJ cet-3919 37 50 value value NOUN cet-3919 37 51 point point NOUN cet-3919 37 52 of of ADP cet-3919 37 53 rolle rolle NOUN cet-3919 37 54 theorem theorem PROPN cet-3919 37 55 and and CCONJ cet-3919 37 56 lagrange lagrange PROPN cet-3919 37 57 mean mean NOUN cet-3919 37 58 value value NOUN cet-3919 37 59 theorem theorem NOUN cet-3919 37 60 is be AUX cet-3919 37 61 a a DET cet-3919 37 62 point point NOUN cet-3919 37 63 in in ADP cet-3919 37 64 the the DET cet-3919 37 65 open open ADJ cet-3919 37 66 interval interval NOUN cet-3919 37 67 , , PUNCT cet-3919 37 68 rather rather ADV cet-3919 37 69 than than ADP cet-3919 37 70 an an DET cet-3919 37 71 arbitrary arbitrary ADJ cet-3919 37 72 point point NOUN cet-3919 37 73 within within ADP cet-3919 37 74 the the DET cet-3919 37 75 interval interval NOUN cet-3919 37 76 or or CCONJ cet-3919 37 77 a a DET cet-3919 37 78 designated designate VERB cet-3919 37 79 point point NOUN cet-3919 37 80 , , PUNCT cet-3919 37 81 in in ADP cet-3919 37 82 other other ADJ cet-3919 37 83 words word NOUN cet-3919 37 84 , , PUNCT cet-3919 37 85 the the DET cet-3919 37 86 two two NUM cet-3919 37 87 mean mean NOUN cet-3919 37 88 value value NOUN cet-3919 37 89 theorem theorem VERB cet-3919 37 90 only only ADV cet-3919 37 91 " " PUNCT cet-3919 37 92 qualitatively qualitatively ADV cet-3919 37 93 " " PUNCT cet-3919 37 94 pointed point VERB cet-3919 37 95 out out ADP cet-3919 37 96 the the DET cet-3919 37 97 existence existence NOUN cet-3919 37 98 of of ADP cet-3919 37 99 the the DET cet-3919 37 100 median median ADJ cet-3919 37 101 point point NOUN cet-3919 37 102 , , PUNCT cet-3919 37 103 rather rather ADV cet-3919 37 104 than than SCONJ cet-3919 37 105 " " PUNCT cet-3919 37 106 quantitatively quantitatively ADV cet-3919 37 107 ” " PUNCT cet-3919 37 108 indicated indicate VERB cet-3919 37 109 the the DET cet-3919 37 110 specific specific ADJ cet-3919 37 111 value value NOUN cet-3919 37 112 of of ADP cet-3919 37 113 the the DET cet-3919 37 114 median median ADJ cet-3919 37 115 point point NOUN cet-3919 37 116 ; ; PUNCT cet-3919 37 117 by by ADP cet-3919 37 118 learning learn VERB cet-3919 37 119 the the DET cet-3919 37 120 application application NOUN cet-3919 37 121 of of ADP cet-3919 37 122 rolle rolle NOUN cet-3919 37 123 and and CCONJ cet-3919 37 124 lagrange lagrange PROPN cet-3919 37 125 mean mean NOUN cet-3919 37 126 value value NOUN cet-3919 37 127 theorem theorem VERB cet-3919 37 128 in in ADP cet-3919 37 129 this this DET cet-3919 37 130 section section NOUN cet-3919 37 131 as as ADV cet-3919 37 132 well well ADV cet-3919 37 133 as as ADP cet-3919 37 134 the the DET cet-3919 37 135 application application NOUN cet-3919 37 136 of of ADP cet-3919 37 137 each each DET cet-3919 37 138 chapter chapter NOUN cet-3919 37 139 in in ADP cet-3919 37 140 the the DET cet-3919 37 141 future future NOUN cet-3919 37 142 , , PUNCT cet-3919 37 143 repeatedly repeatedly ADV cet-3919 37 144 experience experience VERB cet-3919 37 145 the the DET cet-3919 37 146 significance significance NOUN cet-3919 37 147 and and CCONJ cet-3919 37 148 function function NOUN cet-3919 37 149 of of ADP cet-3919 37 150 these these DET cet-3919 37 151 theorems theorem NOUN cet-3919 37 152 in in ADP cet-3919 37 153 calculus calculus NOUN cet-3919 37 154 ( ( PUNCT cet-3919 37 155 pan pan NOUN cet-3919 37 156 , , PUNCT cet-3919 37 157 2014 2014 NUM cet-3919 37 158 ) ) PUNCT cet-3919 37 159 . . PUNCT cet-3919 38 1 2.6 2.6 NUM cet-3919 38 2 . . PUNCT cet-3919 38 3 process process NOUN cet-3919 38 4 teaching teaching NOUN cet-3919 38 5 content content NOUN cet-3919 38 6 and and CCONJ cet-3919 38 7 teaching teaching NOUN cet-3919 38 8 strategy strategy NOUN cet-3919 38 9 : : PUNCT cet-3919 38 10 review review NOUN cet-3919 38 11 : : PUNCT cet-3919 38 12 1 1 NUM cet-3919 38 13 ) ) PUNCT cet-3919 38 14 rolle rolle NOUN cet-3919 38 15 theorem theorem VERB cet-3919 38 16 if if SCONJ cet-3919 38 17 the the DET cet-3919 38 18 function function NOUN cet-3919 38 19 f(x f(x PROPN cet-3919 38 20 ) ) PUNCT cet-3919 38 21 is be AUX cet-3919 38 22 satisfied satisfied ADJ cet-3919 38 23 : : PUNCT cet-3919 38 24 ( ( PUNCT cet-3919 38 25 1 1 X cet-3919 38 26 ) ) PUNCT cet-3919 38 27 be be AUX cet-3919 38 28 continuous continuous ADJ cet-3919 38 29 on on ADP cet-3919 38 30 the the DET cet-3919 38 31 closed closed ADJ cet-3919 38 32 interval interval NOUN cet-3919 38 33 [ [ X cet-3919 38 34 a a X cet-3919 38 35 , , PUNCT cet-3919 38 36 b b NOUN cet-3919 38 37 ] ] X cet-3919 38 38 , , PUNCT cet-3919 38 39 ( ( PUNCT cet-3919 38 40 2 2 X cet-3919 38 41 ) ) PUNCT cet-3919 38 42 be be AUX cet-3919 38 43 guided guide VERB cet-3919 38 44 in in ADP cet-3919 38 45 the the DET cet-3919 38 46 open open ADJ cet-3919 38 47 interval interval NOUN cet-3919 38 48 ( ( PUNCT cet-3919 38 49 a a DET cet-3919 38 50 , , PUNCT cet-3919 38 51 b),(3 b),(3 NOUN cet-3919 38 52 ) ) PUNCT cet-3919 38 53 be be VERB cet-3919 38 54 equal equal ADJ cet-3919 38 55 to to ADP cet-3919 38 56 the the DET cet-3919 38 57 value value NOUN cet-3919 38 58 of of ADP cet-3919 38 59 the the DET cet-3919 38 60 function function NOUN cet-3919 38 61 at at ADP cet-3919 38 62 the the DET cet-3919 38 63 point point NOUN cet-3919 38 64 of of ADP cet-3919 38 65 the the DET cet-3919 38 66 interval interval NOUN cet-3919 38 67 , , PUNCT cet-3919 38 68 that that PRON cet-3919 38 69 is is ADV cet-3919 38 70 f(a)=f(b).then f(a)=f(b).then NOUN cet-3919 38 71 there there PRON cet-3919 38 72 is be VERB cet-3919 38 73 at at ADV cet-3919 38 74 least least ADJ cet-3919 38 75 one one NUM cet-3919 38 76 point point NOUN cet-3919 38 77 (ab (ab NOUN cet-3919 38 78 ) ) PUNCT cet-3919 38 79 , , PUNCT cet-3919 38 80 in in ADP cet-3919 38 81 the the DET cet-3919 38 82 interior interior NOUN cet-3919 38 83 ( ( PUNCT cet-3919 38 84 a a DET cet-3919 38 85 , , PUNCT cet-3919 38 86 b b NOUN cet-3919 38 87 ) ) PUNCT cet-3919 38 88 , , PUNCT cet-3919 38 89 so so SCONJ cet-3919 38 90 that that SCONJ cet-3919 38 91 the the DET cet-3919 38 92 derivative derivative NOUN cet-3919 38 93 of of ADP cet-3919 38 94 the the DET cet-3919 38 95 function function NOUN cet-3919 38 96 f(x f(x PROPN cet-3919 38 97 ) ) PUNCT cet-3919 38 98 at at ADP cet-3919 38 99 that that DET cet-3919 38 100 point point NOUN cet-3919 38 101 is be AUX cet-3919 38 102 equal equal ADJ cet-3919 38 103 to to ADP cet-3919 38 104 zero zero NUM cet-3919 38 105 , , PUNCT cet-3919 38 106 that that PRON cet-3919 38 107 is be AUX cet-3919 38 108 f()=0 f()=0 ADJ cet-3919 38 109 327 327 NUM cet-3919 38 110 http://fanyi.baidu.com/#auto/auto/be http://fanyi.baidu.com/#auto/auto/be NOUN cet-3919 38 111 equal equal ADJ cet-3919 38 112 to to ADP cet-3919 38 113 http://fanyi.baidu.com/#auto/auto/be http://fanyi.baidu.com/#auto/auto/be PROPN cet-3919 38 114 equal equal ADJ cet-3919 38 115 to to ADP cet-3919 38 116 2 2 NUM cet-3919 38 117 ) ) PUNCT cet-3919 38 118 geometric geometric ADJ cet-3919 38 119 meaning meaning NOUN cet-3919 38 120 : : PUNCT cet-3919 38 121 there there PRON cet-3919 38 122 is be VERB cet-3919 38 123 the the DET cet-3919 38 124 tangent tangent NOUN cet-3919 38 125 no no DET cet-3919 38 126 perpendicular perpendicular NOUN cet-3919 38 127 to to ADP cet-3919 38 128 the the DET cet-3919 38 129 x x NOUN cet-3919 38 130 axis axis NOUN cet-3919 38 131 at at ADP cet-3919 38 132 every every DET cet-3919 38 133 point point NOUN cet-3919 38 134 on on ADP cet-3919 38 135 the the DET cet-3919 38 136 closed closed ADJ cet-3919 38 137 interval interval NOUN cet-3919 38 138 [ [ X cet-3919 38 139 a a X cet-3919 38 140 , , PUNCT cet-3919 38 141 b b NOUN cet-3919 38 142 ] ] X cet-3919 38 143 , , PUNCT cet-3919 38 144 and and CCONJ cet-3919 38 145 the the DET cet-3919 38 146 connection connection NOUN cet-3919 38 147 of of ADP cet-3919 38 148 the the DET cet-3919 38 149 two two NUM cet-3919 38 150 ends end NOUN cet-3919 38 151 of of ADP cet-3919 38 152 the the DET cet-3919 38 153 line line NOUN cet-3919 38 154 and and CCONJ cet-3919 38 155 parallel parallel NOUN cet-3919 38 156 to to ADP cet-3919 38 157 the the DET cet-3919 38 158 x x ADJ cet-3919 38 159 axis axis NOUN cet-3919 38 160 of of ADP cet-3919 38 161 the the DET cet-3919 38 162 curve curve NOUN cet-3919 38 163 f(x f(x PROPN cet-3919 38 164 ) ) PUNCT cet-3919 38 165 , , PUNCT cet-3919 38 166 there there PRON cet-3919 38 167 is be VERB cet-3919 38 168 at at ADP cet-3919 38 169 least least ADJ cet-3919 38 170 a a PRON cet-3919 38 171 point point NOUN cet-3919 38 172 c c NOUN cet-3919 38 173 , , PUNCT cet-3919 38 174 making make VERB cet-3919 38 175 its its PRON cet-3919 38 176 tangent tangent NOUN cet-3919 38 177 parallel parallel NOUN cet-3919 38 178 to to ADP cet-3919 38 179 the the DET cet-3919 38 180 x x ADJ cet-3919 38 181 axis axis NOUN cet-3919 38 182 . . PUNCT cet-3919 39 1 figure figure NOUN cet-3919 39 2 2 2 NUM cet-3919 39 3 : : PUNCT cet-3919 39 4 geometric geometric ADJ cet-3919 39 5 sketch sketch NOUN cet-3919 39 6 of of ADP cet-3919 39 7 rolle rolle PROPN cet-3919 39 8 theorem theorem PROPN cet-3919 39 9 lagrange lagrange PROPN cet-3919 39 10 mean mean NOUN cet-3919 39 11 value value NOUN cet-3919 39 12 theorem theorem VERB cet-3919 39 13 : : PUNCT cet-3919 39 14 ( ( PUNCT cet-3919 39 15 1 1 X cet-3919 39 16 ) ) PUNCT cet-3919 39 17 in in ADP cet-3919 39 18 practical practical ADJ cet-3919 39 19 application application NOUN cet-3919 39 20 , , PUNCT cet-3919 39 21 the the DET cet-3919 39 22 condition condition NOUN cet-3919 39 23 ( ( PUNCT cet-3919 39 24 3 3 NUM cet-3919 39 25 ) ) PUNCT cet-3919 39 26 of of ADP cet-3919 39 27 rolle rolle NOUN cet-3919 39 28 's 's PART cet-3919 39 29 theorem theorem NOUN cet-3919 39 30 can can AUX cet-3919 39 31 not not PART cet-3919 39 32 be be AUX cet-3919 39 33 satisfied satisfied ADJ cet-3919 39 34 , , PUNCT cet-3919 39 35 so so ADV cet-3919 39 36 its its PRON cet-3919 39 37 application application NOUN cet-3919 39 38 is be AUX cet-3919 39 39 limited limited ADJ cet-3919 39 40 . . PUNCT cet-3919 40 1 if if SCONJ cet-3919 40 2 the the DET cet-3919 40 3 condition condition NOUN cet-3919 40 4 ( ( PUNCT cet-3919 40 5 3 3 X cet-3919 40 6 ) ) PUNCT cet-3919 40 7 is be AUX cet-3919 40 8 removed remove VERB cet-3919 40 9 , , PUNCT cet-3919 40 10 it it PRON cet-3919 40 11 is be AUX cet-3919 40 12 the the DET cet-3919 40 13 lagrange lagrange PROPN cet-3919 40 14 mean mean NOUN cet-3919 40 15 value value NOUN cet-3919 40 16 theorem theorem VERB cet-3919 40 17 to to PART cet-3919 40 18 be be AUX cet-3919 40 19 introduced introduce VERB cet-3919 40 20 . . PUNCT cet-3919 41 1 lagrange lagrange NOUN cet-3919 41 2 mean mean PROPN cet-3919 41 3 value value NOUN cet-3919 41 4 theorem theorem VERB cet-3919 41 5 : : PUNCT cet-3919 41 6 if if SCONJ cet-3919 41 7 the the DET cet-3919 41 8 function function NOUN cet-3919 41 9 f(x f(x PROPN cet-3919 41 10 ) ) PUNCT cet-3919 41 11 is be AUX cet-3919 41 12 satisfied satisfied ADJ cet-3919 41 13 : : PUNCT cet-3919 41 14 ( ( PUNCT cet-3919 41 15 1 1 X cet-3919 41 16 ) ) PUNCT cet-3919 41 17 continuous continuous ADJ cet-3919 41 18 on on ADP cet-3919 41 19 the the DET cet-3919 41 20 closed closed ADJ cet-3919 41 21 interval interval NOUN cet-3919 41 22 [ [ X cet-3919 41 23 a a X cet-3919 41 24 , , PUNCT cet-3919 41 25 b b NOUN cet-3919 41 26 ] ] X cet-3919 41 27 , , PUNCT cet-3919 41 28 ( ( PUNCT cet-3919 41 29 2 2 X cet-3919 41 30 ) ) PUNCT cet-3919 41 31 be be AUX cet-3919 41 32 guided guide VERB cet-3919 41 33 in in ADP cet-3919 41 34 the the DET cet-3919 41 35 open open ADJ cet-3919 41 36 interval interval NOUN cet-3919 41 37 ( ( PUNCT cet-3919 41 38 a a DET cet-3919 41 39 , , PUNCT cet-3919 41 40 b b NOUN cet-3919 41 41 ) ) PUNCT cet-3919 41 42 , , PUNCT cet-3919 41 43 then then ADV cet-3919 41 44 there there PRON cet-3919 41 45 is be VERB cet-3919 41 46 at at ADV cet-3919 41 47 least least ADV cet-3919 41 48 one one NUM cet-3919 41 49 point point NOUN cet-3919 41 50 (a<