-浅谈导在中学数学中的应用.doc

\ PAGE   PAGE 10 本科毕业论文 浅谈导数在中学数学中的应用 姓 名 系 别 数学与计算机科学系 专 业 数学与应用数学 班 级 学 号 指导教师 答辩日期成 绩 浅谈导数在中学数学中的应用 内容摘要 导数是数学学习中的重要内容，是高等数学与初等数学的纽带。许多初等数学不能解决或难以解决的问题，通过建立数学模型，把初等数学中的问题变为函数问题，用函数的思想，利用导数研究其性质，充分发挥导数的工具性和应用性，使问题的解决有更广泛的思维性。许多中学问题，例如函数（解析式、值域、最（极）值、单调区间等）问题、切线问题、不等式问题以及数列问题都可以运用到导数。本文一一对其进行了阐述，期望通过对导数在新课程中的地位以及在中学数学解题应用中的探讨、研究，拓宽学生的解题思路，提高学生分析和解决问题的能力。 【关键词】导数 新课程 应用 A Simple Comment on the Application of Derivative in the secondary School Mathematics Curriculum Abstract The derivative is the mathematical study of the important content, is the higher mathematics and elementary mathematics. Many elementary mathematics to be solved or difficult to resolve the problem, through the establishment of the mathematical model, the elementary mathematics problem into the function problem, using the idea of function, using derivative to study its nature, give full play to the derivative tools and applications, and makes the solution of problem with broader thinking. Many of the secondary problems, such as function (analytic type, range, the ( very ) value, monotone interval ) problem, tangent problem, inequalities and sequence can be applied to the derivative. This article one one of it were analyzed, with the derivative in the new curriculum in the position as well as in the middle school mathematics problem solving application discuss, study, broaden students problem-solving ideas, improve students ability to analyze and solve problems. 【Key words】derivative new curriculum application 目 录  TOC \o 1-3 \h \z \u  HYPERLINK \l _Toc323332734 引言 HYPERLINK \l _Toc323332749  (1)  HYPERLINK \l _Toc323332735 一、导数的概念 HYPERLINK \l _Toc323332749  (1)  HYPERLINK \l _Toc323332736 （一）定义 (1)  HYPERLINK \l _Toc323332737 （二）几何意义 (1) (三）利用定义求导数的步骤 HYPERLINK \l _Toc323332749  (1)  HYPERLINK \l _Toc323332742 （四）注意 (2)  HYPERLINK \l _Toc323332743 （五）导数的四则运算 (2