浅析导数在高中数学中的应用

Analysis of the application of derivative in senior high school mathematics

导数是微积分中的基本概念,是近代数学的基础。导数的引入,为很多问题提供了新的视野,在高中数学教学中,导数在很多方面都有着重要应用。一线高中数学教师要充分认识到导数思想对学生学习的重要意义,将导数作为工具融入到其他知识的教学中。本文主要从函数单调性、函数极值、函数最值、绘制函数图像、不等式证明、数列研究等六个方面阐述导数的重要应用,以期给一线数学教师及高中学生提供参考。

derivative is the basic concept of calculus and the foundation of modern mathematics. The introduction of derivative provides a new perspective for many problems. In mathematics teaching in senior high school,derivative has important application in many aspects. First line high school mathematics teachers should fully realize the importance of derivative thought to students' learning,and integrate derivative as a tool into the teaching of other knowledge. This paper expounds the important application of derivative from six aspects,such as function monotonicity,function extreme value,function maximum value,drawing function image,inequality proving and number sequence research,in order to provide reference for first-line mathematics teachers and senior high school students.