与中值定理相关的辅助函数的一个构造法  

A Universal Construction Method of Auxiliary Functions Related to Mean Value Theorems

作　　者：杨红莉 李士垚[3] 于红 曾宪阳 YANG Hong-li1,2, LI Shi- yao3, YU Hong3, ZENG Xian-yang2,4(1. Dept, of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, China;2. Dep. of Mathematics, Nanjing University, Nanjing 210093, China;3. School of Electric Power Engineering, Nanjing Institute of Technology, Nanjing 211167, China;4. Industrial Center, Nanjing Institute of Technology, Nanjing 211167, Chin)

机构地区：[1]南京工程学院数理部,江苏南京211167 [2]南京大学数学系,江苏南京210093 [3]南京工程学院电力工程学院,江苏南京211167 [4]南京工程学院工业中心,江苏南京211167

出　　处：《南京工程学院学报（自然科学版）》2018年第1期66-70,共5页Journal of Nanjing Institute of Technology(Natural Science Edition)

基　　金：国家自然科学基金项目(11701274);江苏省自然科学基金项目(BK20170760);南京工程学院创新基金重大项目(CKJA201410)

摘　　要：与中值定理相关命题的证明关键点和难点是构造合适的辅助函数.目前存在大量的构造方法,但适用性较低,在具体实践时没有一个通用性好的构造法.分析现有的一些构造方法的内在联系;通过分析构造法的本质,引入守恒量构造法;通过多个例子,证明守恒量构造法适用性强、使用范围较广、构造简单,是一个有效的构造方法.Propositions related to mean value theorems are an integral part of examination contents of advanced mathematics. The key and difficulty of the proof of this kind of proposition are to construct proper auxiliary functions. At present, a great number of construction methods have been presented, but their applicability is much small. No universal method with good performances is available at present. This paper, firstly, studies internal relationships between some existing construction methods, and then introduces the conserved quantity construction method by analyzing the nature of these construction methods. Finally, several examples are given to show that the construction method of conserved quantity has strong applicability and is much simple. It can be called a universal construction method for constructing auxiliary functions.

关 键 词：微分中值定理 辅助函数 构造法 

分 类 号：O172.1[理学—数学]