罗尔定理中辅助函数的构造法  

The Construction of Auxiliary Functions in Rolle's Theorem

作　　者：郭元春 陈思源[1] 马晓燕[2] Guo Yuanchun;Chen Siyuan;Ma Xiaoyan(Xi'an SiYuan University,Department of Basic Course,ShanxiXi’an 710038;Xi'an SiYuan University,Higher Education Marketing Research Center Shanxi,Xi’an 710038)

机构地区：[1]西安思源学院基础部,陕西西安710038 [2]西安思源学院高等教育营销研究中心,陕西西安710038

出　　处：《科技风》2022年第32期106-108,共3页

基　　金：西安思源学院校级教改项目,专升本高等数学课程创新型教材开发研究与实践(SYGZJG22001)。

摘　　要：辅助函数的构造是利用罗尔定理证明微分中值等式的关键。本文采用逆向思维法对微分中值问题中构造辅助函数的常见题型作归纳和总结,这种解法对利用罗尔定理证明的中值等式问题具有一定的普遍适用性。The construction of auxiliary function is the key to prove the differential mean value equation by Rolle's theorem.In this paper,the general problems of constructing auxiliary functions in differential mean value problems are summarized by using reverse thinking method.This method has widely applicability to the mean value equality problem proved by Rolle's theorem.

关 键 词：罗尔定理 辅助函数 微分方程 通解 逆向思维法 

分 类 号：G63[文化科学—教育学]