关于Lagrange微分中值定理的逆问题  

On Inverse Problem of Lagrange's Differential Mid-vaIue Theorem

作　　者：王良成[1] 白海[2] 杨明硕[1] 

机构地区：[1]重庆师范大学涉外商贸学院,重庆401520 [2]重庆理工大学数学与统计学院,重庆400054

出　　处：《大学数学》2012年第5期140-143,共4页College Mathematics

基　　金：重庆师范大学涉外商贸学院"高等代数"精品课程项目(ZLGC201205)

摘　　要：近年来,若干文章对"Lagrange微分中值定理的逆问题"进行了讨论,但其表述均不完整,且证明也较繁琐。本文使用严格凸(严格凹)函数的性质,给出该问题一个条件较弱且表述较完整的结果,其证明也较简洁.In recent years, the some papers discuss the“ inverse problem of Lagrang＇s differential mid-value theorem ”, but their expressions are not complete, and their proof are more verbose. In this paper, by the properties of strictly convex （strictly concave） function, we give a weak condition and more complete results for “ inverse problem of Lagrang＇ s differential mid-value theorem ”, and its proof is more concise.

关 键 词：Lagrange微分中值定理 严格凸函数 严格凹函数 逆问题 

分 类 号：O178[理学—数学]