英语翻译拉格朗日乘数法一直都是人们研究很多的数学对象.在许多极值问题中,函数的自变量往往要受到一些条件的限制,比如,要设计一个容积为 V的长方体形开口水箱,确定长、宽和高,使水

英语翻译拉格朗日乘数法一直都是人们研究很多的数学对象.在许多极值问题中,函数的自变量往往要受到一些条件的限制,比如,要设计一个容积为 V的长方体形开口水箱,确定长、宽和高,使水
英语翻译
拉格朗日乘数法一直都是人们研究很多的数学对象.在许多极值问题中,函数的自变量往往要受到一些条件的限制,比如,要设计一个容积为 V的长方体形开口水箱,确定长、宽和高,使水箱的表面积最小.设水箱的长、宽、高分别为 x,y,z,则水箱容积V=xyz 焊制水箱用去的钢板面积为 S=2xz+2yz+xy .实际上是求函数 S 在 V 限制下的最小值问题.这类附有条件限制的极值问题称为条件极值问题,其一般形式是在条件限制下,求函数F的极值.
本文首先介绍了拉格朗日乘数法及其拓展,给出了多元函数条件极值的必要条件,并利用它求解了多元函数的条件极值问题.而后利用正定二次型理论,证明了多元函数条件极值的一个充分条件,并给出了其应用的例子.

英语翻译拉格朗日乘数法一直都是人们研究很多的数学对象.在许多极值问题中,函数的自变量往往要受到一些条件的限制,比如,要设计一个容积为 V的长方体形开口水箱,确定长、宽和高,使水
Lagrange multiplier method has been the research object by people.In many Extremum problems,the independent variable of fouctions were always been limited by some conditions,for example,if you want to design a finite shape box which volume is V,how the length,width and height values of the length,width and height are when the surface of the box is least.Assumed the length,width and height is x,y,z,and v=xyz,the steel which used to weld the box S=2xz+2yz+xy.Actually it is equal to the least-value problem about S is limited by V.This kind of Extremum problems is called Extreme conditions ,its general form is go for F's extreme value by some conditions limiting.
This paper introduce Lagrange multiplier method and its expandings first,and show the necessary condition of Multivariate function's extreme value,and use it to solve the Multivariate function's extreme value problem.Then using Positive definite quadratic theory to prove a sufficient condition of Multivariate function's extreme value problem and show some examples about it.

Lagrange the multiplicator law has been the people studies many mathematical objects. In many minimum problems, the function independent variable often needs to receive some conditions the limit, for ...

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Lagrange the multiplicator law has been the people studies many mathematical objects. In many minimum problems, the function independent variable often needs to receive some conditions the limit, for instance, must design a volume is V rectangle build aperture water tank, firmly fixed-length, affable high, causes water tank's surface area to be smallest. Supposes water tank's length, the width high, respectively is x, y, z, then water tank volume V=xyz welds the steel plate area which the system water tank uses is S=2xz+2yz+xy. In fact is asks function S under V limit minimal problem. This kind of with proviso limit's minimum problem is called the condition minimum problem, its general form is under the condition limit, asks function F the extreme value. this article first introduced the Lagrange multiplicator law and the development, have given the function of many variables condition extreme value essential condition, and solved the function of many variables condition minimum problem using it. Then using the Zhengding quadratic form theory, had proven a function of many variables condition extreme value's sufficient condition, and has given its application example.

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楼上的GOOGLE翻译太有爱了。

设圆柱体的底面圆的半径为r，圆柱体的高度为h 。
依题意V=πr*r*h
S=2πr*r + 2πr*h
联立之后求S的导数，令S导数为0
求出r值，h值
然后根据r，h值设计圆柱体