浅谈利用导数求解函数单调性

Introduction to Derivative Solving Function Monotonicity

单调性是函数的几大性质之一,而且也是各阶段数学学习的重要内容.一般来说,函数单调性定义较为简单易懂,但是如果直接利用其定义去求解其单调性,那么其中涉及的函数变形较为复杂,且超过普通学生的学习范围和能力要求.因此利用导数求解一直是函数单调性学习的重要方式,同样它也是学生函数性质掌握情况重要考量标准.在教学中,如何运用导数求解函数单调性是师生共同的教学重点,也是巩固其他学科学习理论的重要基石.本文探讨了利用导数求解一元函数单调性的基本注记.

Monotonicity is one of the several properties of function, but also the important content of mathematics learning at all levels. In general, functional monotonicity definition is relatively easy to understand, but if direct use its definition to solve its monotonieity, so which involves the function of deformation is relatively complex, and beyond the scope and capacity requirements of students. So derivative solving functional monotonicity learning has been an important way, it also is the student knowledge about important consideration standard function properties. Function monotonicity teach- ing how to use derivative to solve it is the teaching emphasis both teachers and students.