保山学院学报

微分中值定理是微分学的基本定理,是沟通函数与导数之间的桥梁。微分中值定理的应用是一个非常广泛的课题,应用微分中值定理的基本方法是广泛使用辅助函数。主要介绍如何在证明题中巧妙地选用和构造辅助函数,并利用构造辅助函数的方法求解几个微分中值定理的相关实例。

The differential mean value theorem is the fundamental theorem of the differential calculus.It is the bridge between the function and the derivative.The application of the differential mean value theorem is a very extensive subject.The basis method of the differential mean value theorem’s apply is extensive constructing auxiliary function.This paper is main to introduce how to select and construct auxiliary function in proofs,and use this metheod to solve some related instances of the differential mean value theorem.