条件极值与均值不等式求最值的比较  

Comparison of the Maximum Value of Conditional Extremum and Mean Inequality

作　　者：杜先云[1] 任秋道 王敏 文华燕 Du Xianyun;REN Qiudao;WANG Min;WEN Huayan(College of Mathematics of Chengdu University of Infomlation Technology,Chengdu,Sichuan 610225;Department of Mathematics and Physics,Mianyang Teachers College,Mianyang,Sichuan 621000;City College of Southwest Science University,Mianyang,Sichuan 621000)

机构地区：[1]成都信息工程学院数学学院,四川成都610225 [2]绵阳师范学院数理学院,四川绵阳621000 [3]西南科技大学城市学院,四川绵阳621000

出　　处：《绵阳师范学院学报》2018年第8期30-33,46,共5页Journal of Mianyang Teachers＇ College

基　　金：四川省教育厅基金资助(16ZB0314)

摘　　要：利用均值不等式证明不等式需要构造n个可能相等的正数,特别是用来求最大(小)值,就必须构造n个相等的正数.对于很多学生来说,这比较困难.本文利用求条件极值的方法简单证明了均值不等式和加权均值不等式,从而一些用均值不等式证明的不等式就可以用条件极值来证明,特别是含有等号的严格不等式可用求条件极值的方法来证明.Using the mean of inequality to prove an inequality needs to construct positive numbers that may be equal. Especially for maximum（ small） values,equal positive numbers must be constructed. For a lot of students,this is more difficult. In this paper,the mean inequality and weighted mean inequality are simply proved by the method of finding conditional extremum. Thus,some inequalities proved by the mean inequality can be proved by conditional extremum. In particular,strict inequalities with equal signs can be proved by the conditional extremum.

关 键 词：不等式 均值不等式 最大值 最小值 

分 类 号：O186.1[理学—数学]