微分中值定理在不等式证明中的应用

The Application of the Mean Value Theorem in the Proof of Inequality

微分中值定理是微分学的基本定理,也是微分学理论的核心.它是研究函数在区间上整体性质的有力工具,有着广泛的应用,而且对后续内容的学习也有着深远的影响.而微分中值定理一个典型的应用就是在不等式证明的问题上.本文主要研究了微分中值定理在几种不等式证明中的应用.

The value theorem of differentiation is the fundamental theorem of differential learning and the core of differential theory. It is a powerful tool for the integrative quality of the research function in the interval and extensive application. It also has a far-reaching influence on the study of the following content. A typical application of the differential mean value theorem is in the problem of inequality proof. Therefore,the author will apply some examples to show the application of the differential mean value theorem in the inequality proof.