微分中值定理及其应用内容摘要微分中值定理在数学分析中占有重要地位,为我们研究函数提供了有力工具.本文首先介绍了微分中值定理的历史发展和应用前景,其次详细阐述了微分中值定理的具体内容并给出了各定理的证明方法,然后总结归纳了中值定理之间的联系,最后通过分类举例来体现微分中值定理在解决不同函数问题时的应用,进一步加深了对微分中值定理的认识和学习.【关键词】微分中值定理 中值问题 联系 单调性 不等式1Differential mean value theorem and its applicationAbstractDifferential mean value theorem plays an important role in mathematical analysis and provides a powerful tool for us to study functions.This paper first introduces the historical development and application prospect of the differential mean value theorem.Secondly, it elaborates the specific contents of the differential mean value theorem and gives the proving methods of each theorem.And then it summarizes the connection between the mean value theorem.Finally, the application of differential mean value theorem in solving different function problems is illustrated by classification examples, which further deepens the understanding and learning of differential mean value theorem. 【Key Words】Differential mean value theorem The median problem Relation Monotonicity Inequation2目录一、引 言..............................................5二、微分中值定理及其证明...............................6(一)费马定理............................................................6(二)罗尔(ROLLE)中值定理..................................................6(三)拉格朗日（LAGRANGE）中值定理..........................................7(四)柯西(CAUCHY)中值定理.................................................7三、微分中值定理之间的联系.............................8四、微分中值定理的应用.................................10(一)利用微分中值定理来解决方程根是否存在的问题.........................10(二)通过运用微分中值定理来计算复杂极限.....................
