中值定理在证明中的应用

Application of Isovalue Theorem in Identification

在高等数学的教学过程中,证明函数不等式和等式是涵盖面很大的一类问题,证明的方法繁多又非常灵活,因此显得比较困难。本文要介绍的是如何利用中值定理证明不等式和等式,对各种不同特点的问题类型进行分析、总结,并结合典型例子给出恰当的方法,对提高证明题的能力有很大的帮助。

In terms of teaching advanced mathematics, identifying non-equation and equation of function is a series of problems, since its methods of identification are alternative and flexible, it seems difficult to be worked out and the solutions appear not so easily to be found. The article focuses on how to identify equation and non-equation by adopting Isovalue Theorem, analyzing and summarizing the solutions according to problems with different characteristics, combining typical examples to show the reasonable solutions to them. It can improve the ability of identification greatly.