再论Cauchy微分中值定理的逆问题  

Further Discuss Inverse Problem of Cauchy's Differential Mid-VaIue Theorem

作　　者：王良成[1] 马秀芬[1] 杨明硕[1] WANG Liang-Cheng MA X iu- fen YANG Ming-Shuo(Chongqing Normal University, Foreign Trade And Business College, Chongqing 401519, China)

机构地区：[1]重庆师范大学涉外商贸学院,重庆401520

出　　处：《大学数学》2016年第5期101-104,共4页College Mathematics

基　　金：重庆师范大学涉外商贸学院重点科研项目(KY2015001)

摘　　要：文[1]给出了"Cauchy微分中值定理"中值点唯一的条件,并得到了其逆定理的较弱表述.继续文[1]的工作,利用闭区间上连续函数的性质及函数的单调性,解决了其逆定理中端点的唯一性.In the paper [1], the condition of unique mid-value point for ＂ Cauehy＇s differential mid-value theorem ＂ is given, and its the inverse theorem of weak expression is obtained. In this paper, we continue to the work of the paper [1]. By the properties of continuous functions on closed interval and monotonicity of function, we solve the uniqueness of end-point for its the inverse theorem.

关 键 词：CAUCHY微分中值定理 严格单调性 左右导数 导数 逆问题 

分 类 号：O178[理学—数学]