浅谈导数在高中数学中主要的应用摘要：导数作为研究函数的单调性、变化快慢、最值和极值等问题的最方便的工具，在高中数学中处于一个非常重要的位置。导数的学习为解决高中数学问题提供了新的依据和方法，使学生的数学思维得到发展、解题能力得到提升。导数作为解决高中数学问题的重要工具之一，其相关知识在高考中占有十分重要的地位。同时导数作为微积分的重要内容之一，被认为是现代数学的基本概念，体现了微积分的基本思想，为之后对高等数学的学习奠定了基础。本文将首先阐述高中数学中导数的基本情况，然后通过对高考试题的分析，采取分类讨论的方式，对导数在高中数学中的主要应用进行总结和归纳。包括导数在几何中的应用、导数在函数中的应用、导数在不等式中的应用三个方面，其中较为重要的是导数在几何中的应用和导数在函数中的应用。导数在几何中的应用主要是考查对导数的几何意义的理解和运用；对于导数在不等式中的应用，其实质是导数与函数性质的综合应用。导数能够定量地刻画函数局部变化，是研究函数各种性质的有效工具，本文将从函数的单调性、极值、最值和零点问题四个方面对其进行总结。关键词：导数：高中数学：数学问题A brief Discussion on the main Application of Derivative in SeniorHigh School MathematicsAbstract:As the most convenient tool to study the problems of the monotonicity,thespeed of change,the maximum and the extreme value of function,derivative is in avery important position in senior high school mathematics.The learning of derivativeprovides a new basis and approach for solving problems in high school mathematics,which can develop the mathematical thinking and improve the ability of solvingproblems of students.As one of the important tools to solve high school mathematicsproblems,derivative plays an very important role in the college entrance examination.At the same time,as one of the important contents of calculus,derivative isconsidered as the basic concept of modern mathematics,which embodies the basicideas of calculus and lays the foundation for the later learning of higher mathematics.In this paper,I will first elaborate the basic situation of derivative in senior highschool mathematics,and then through the analysis of college entrance examinationquestions.The main application of derivative in senior high school mathematics issummarized and concluded by the way of classified discussion.It includes threeaspects:the application of derivative in geometry,the application of derivative infunction and the application of derivative in inequality,among which the applicationof derivative in geometry and the application of derivative in function are moreimportant.The application of derivative in geometry is mainly to examine theunderstanding and application of the geometric meaning of derivative.For theapplication of derivative in inequality,its essence is the comprehensive application ofderivative and function properties.Derivative is an effective tool to study the variousproperties of function,which can quantitatively describe the local change of function.In this paper,I will summarize it from the monotonicity,extreme value,maximumvalue and zero point of function.Key words:Derivative;High school mathematics;Mathematical problem目录1绪论11.1选题的背景及意义…11.2国内外研究现状1II2高中数学中导数的基本情况.22.1导数在高中教材中的地位.22.2导数在高中教材中的内容..32.1.1导数的概念32.1.2导数的计算.…32.3近3年高考（理科）试题对导数的考查情况43导数在高中数学中主要的应用.53.1导数在几何中的应用…53.2导数在函数中的应用…63.2.1利用导数判断函数的单调性.63.2.2利用导数求函数的极值.83.2.3利用导数求函数的最值…93.2.4利用导数求函数的零点，93.3导数在不等式中的应用.11参考文献…