一种二元函数极值存在的充分条件的简单证明方法

A simple proof of sufficient condition for the existence of extreme value of functions of two variables

在数学分析和高等数学的教材中都用泰勒公式证明二元函数存在极值的充分条件,很复杂。本文不使用泰勒公式,给出该条件一个简单、易懂的证明方法。

In mathematics analysis and higher mathematics textbooks,the sufficient condition for the existence of extreme value of functions of two variables is proved by means of Taylor’s formula.The proof is very complicated.In this paper,a simple and easy-to-understand proof of the sufficient condition is presented without using Taylor’s formula.