基本初等函数的凸性及其应用

The Convexity of Elementary function and its Application

本文较系统地介绍了函数的凸性定义,凸性的判定及凸性的性质,指出了基本初等函数的凸性,并运用基本初等函数的凸性证明了中学里常见的算术几何平均值不等式和一组三角不等式。

This article makes a systematic analysis of the definition,judgment and properties of convex function, and points out the convexity of elementary function. And by using the convexity of elementary function if also demonstrates the arithmetic mean and geometric mean inequality and a group of triangular inequality which are aften found in the middle school.