偶函数在零点处导数为零的六种解法

Six Approaches for Derivative of Even Functions at Zero

以一道证明偶函数在零点处导数为零的习题为例,分别使用链式法则、导数定义,带Peano型余项的泰勒公式等知识,给出6种解法,旨在培养学生分析问题和解决问题的能力.

It is known that the derivative of an even function at zero, if exists, is zero. In this paper, we provide six approaches to this fact by using the chain rule, the definition of derivative, and Taylor formula with Peano remainder, etc. These approaches can be useful for training students＇ ability of analyzing and solving problems.