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多元函数条件极值的几种求解方法
摘 要:本篇文章主要对多元函数条件极值的几种求解方法进行概括,多元函数条件极值是多元函数微分学的重要组成部分;以及探讨多元函数条件极值在证明不等式、物理学、生产销售等问题上的应用。本文主要研究多元函数条件极值的几种求解方法,如直接代入法、拉格朗日乘数法、柯西不等式、梯度法、数形结合法等;并对拉格朗日乘数法中着重介绍全微分和二阶偏导数即Hesse矩阵法等;以便在解决相应的问题时能得以参考、借鉴,更快、更准确地找到解决问题的方法。
关键词:拉格朗日乘数法;柯西不等式;极值;应用

Abstract:In this paper we summary mainly several kind of methods about conditional extremum of function of several variables,this topic is the important constituent part;and discuss the applications of some problems about the proof of inequality,physics,production and market etc..
In our paper we study mainly several kind of methods about conditional extremum of function of several variables,such as direct substitution method,Lagrange multiplier method,Cauchy inequality,gradient method,numbers and figures combined method etc.;and introduced mainly total differentiation and second partial derivative,i.e. Hesse matrix method etc. about Lagrange multiplier method and in order to reference and use for reference in solving corresponding problems,and find the methods of solving problems faster and more precise.
Key words:Lagrange multiplier method,Cauchy inequality,extremum,applications. |
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