微分中值定理及其应用摘 要 本 文 首 先 介 绍 了 微分中值定理的发展历程，叙述了微分中值定理的内容和证明方法，并描述了三个定理的几何意义与内在联系，然后阐述了与定理相关的一些性质，最后举例说明定理的应用，进一步探索函数与导函数之间的关系。将大学教材与收集到的例题相结合，充分展现微分中值定理的应用性。该定理是联系函数与导函数之间的一根关系绳，并且我们在讨论时往往是根据导函数在区间所表现来的性质来研究函数本身的性质， 从 定理内容本身、形式、数学含义和证明等各个方面去分析微分中值定理之间的联系，展现它们的理论价值与重要意义。关键词 微分中值定理 罗尔定理 拉格朗日中值定理 柯西中值定理 构造函数IMean Value Theorem and Its ApplicationsAbstract In this article, the course of the development of the differential mean theorem is presented, the specific content and the method of proof of the differential mean theorem are described, and the geometric meaning and the internal relationships of the three theorems are described. Then some properties related to the theorem are explained. And, illustrates the application of the theorem using examples to further explore the relationship between the function and the derived function. The combination of university teaching materials and collected examples fully shows the applicability of the differential mean theorem. The sentence is a relationship rope between the relationship function and derivative function. We often examine the properties of the function itself based on the properties of the derivative function in the interval. We analyze the relationship between the differential mean sets from content, form, mathematical meaning and proof of the set and show their theoretical value and important meaning.Key words Differential median theorem,Rolle's theorem,Lagrange median theorem,Cauchy median theorem,constructorII目 录1 引言...................................
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