微分中值定理解题区间和函数构造探索  

Exploration on Interval and Function Construction of Differential Mean Definite Understanding Problem

作　　者：杨雄[1] 肖靓[1] Yang xiong;Xiao liang(Loudi Vocational Technical College,Loudi Hunan 417000)

机构地区：[1]娄底职业技术学院,湖南娄底417000

出　　处：《保山学院学报》2020年第2期25-28,共4页JOURNAL OF BAOSHAN UNIVERSITY

基　　金：2018年度湖南教育科学规划一般资助课题阶段性研究成果(项目编号:XJK18BZY025)。

摘　　要：微分中值定理在解题过程中,已知条件大部分不能直接满足定理,即不能直接使用定理求解,需要构造满足条件的区间或函数,此过程相当于对中值定理公式的推广或对中值定理证明方法的借鉴,这种解决问题的方法被称为辅助区间法和辅助函数法。对区间和函数的构造方法进行分析,厘清区间和函数构造的思路,进而拓宽微分中值定理的应用教学和学习思路,促进对微分中值定理的理解和应用。In the process of solving the problem by differential median theorem,most of the known conditions can not directly satisfy the theorem,that is,they cannot be solved directly by using the theorem,so it is necessary to construct an interval or function that satisfies the condition.This process is equivalent to the generalization of the formula of the median theorem or the reference to the method of proving the median theorem,and the method is called the auxiliary interval method and the auxiliary function method.This paper analyzes the construction methods of interval and function,clarifies the idea of interval and function construction,and then broadens the teaching and learning ideas of application of differential median theorem,and promotes the understanding and application of differential median theorem.

关 键 词：微分中值定理 辅助区间法 辅助函数法 

分 类 号：O13[理学—数学]