函数、导数与不等式是中学数学中最重要的内容,近年来函数导数不等式题型常作为高考压轴题,对考生来说如何根据所要证的不等式构造恰当的函数,利用导数研究函数的单调性,借助单调性比较函数值的大小,以期达到证明不等式的目的是一个难点.本文以今年全国I卷(乙卷)理科数学第21题和几道模拟试题为例,说明如何构造一个好函数,求 Functions, Derivatives and Inequalities are the most important contents in the middle school mathematics. In recent years, the function derivative inequality is often used as the finale of college entrance examination. How to construct appropriate functions for the candidates according to the inequalities of the required evidences, It is a difficult point to compare the function values ​​with monotonous ones in order to achieve the purpose of proving inequalities.This paper takes the 21st National Science and Technology Volume I and some simulated test questions as examples to illustrate how to construct a good function,