从中值等式的证明看微分中值定理的教学  

Design Teaching Method of Mean Value Theorems from the Proof of Mean Value Equation

作　　者：范周田[1] 张汉林[1] FAN Zhou-tian;ZHANG Han-lin(College of Science, Beijing University of Technology, Beijing 100124,China)

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《大学数学》2017年第6期50-54,共5页College Mathematics

摘　　要：中值等式的证明是微积分教学的难点.本文从分析罗尔定理的条件与结论的关系出发,介绍两种构造辅助函数的方法及其应用.教学设计是用尽量简单的讲授达到会应用中值定理的目的.The proof on mean value theorem is the main difficult point in the process of teaching.This paper consider Rolle theorem as the first step,introduce two methods and its applications of making auxiliary functions.The teaching design is that using simple teaching attains the goal of applied the mean value theorems.

关 键 词：微分中值定理 辅助函数 常数k法 因子法 常数变易法 

分 类 号：O172.1[理学—数学]