摘 要微分中值定理是一系列中值定理的总称，它是研究函数的有力工具，能够很好地帮助我们分析和研究函数与其导函数的性质。本文简单介绍三个微分中值定理的内容与发展历史，并分析了他们之间的相互联系。通过收集、解答近些年中学数学试卷中的题目，并联系中学数学的教学内容。给出了若干微分中值定理在中学数学中的应用，并且对解答中的应用技巧进行分析和研究。我们通过掌握具体的知识、技能和方法，从而培养其思维能力和创新意识，并找到中学教材内容和高数的衔接点。更好的分析所遇到的深奥的问题，在解题中提供更宽阔的思路。关键词：微分中值定理；中学数学；函数；应用；AbstractDifferential mean value theorem is a general term of a series of mean value theorems. It is a powerful tool for studying functions and can help us to analyze and study the properties of functions and their derivative functions. This paper briefly introduces the contents and development history of three differential mean value theorems, and analyzes their interrelations. Through collecting and answering the questions in the middle school mathematics papers in recent years, and connecting the teaching content of middle school mathematics. The application of some differential mean value theorems in middle school mathematics is given, and the application skills in the solution are analyzed and studied. By mastering the specific knowledge, skills and methods, we can cultivate their thinking ability and innovative consciousness, and find the connection point between the content of middle school textbooks and high mathematics. Better analysis of the profound problems encountered, in solving the problem to provide a broader thinking.Keywords: differential mean value theorem; middle school mathematics; function; application;目 录第一章 绪 论.....................................................11.1 研究意义...................................................11.2 研究背景......
