一道函数极值的研究摘要 本文用一道函数极值的题目,研究了有关函数极值的判定问题,以及推广到多元函数.对函数极值的概念和判定条件进行分析,知道求解函数极值的一些方法,比如:几何模型、梯度法、黑赛矩阵、导数等.尤其是,我们能够熟练使用拉格朗日乘数法去求解那些有约束条件限制的函数的极值,并以这三元函数为基础,推广到 n 元函数,研究这 n 元函数的条件极值问题.本文给出函数极值的相关概念,接着以二元函数为主,探究二元函数极值的判定方法.最后,可以得到根据拉格朗日乘数法算出函数的驻点,接着利用判定方法解决驻点的极值情况,最终得出函数的极值.关键词 多元函数 二元函数 条件极值 极值 拉格朗日乘数法 判定方法 The study of extremum of a function Abstract This paper deals with the determination of the extremum of a function and extends to multiple-variable functions.This paper analyzes the concept and decision condition of the function extremum, decision condition of the function extremum, and knows some methods to solve the function extremum. such as geometric model, gradient method, Hesse matrix, derivative, etc. In particularly, we can use Lagrange multiplication to solve the extremum of the constrained function, and based on this function with three variables, extended to n-variate functions, and study the conditional extremum of n- variate functions. In this paper, the concept of function extremum are given. Then, the determination method of extreme value of binary function is studied mainly by binary function. Finaly, Lagrange multiplication can be used to calculate the stagnation point of the function, and then the determination method can be used to solve the extremum of the stagnation point.Key words multiple-variable functions, binary function, conditional extremum, extremum, lagrange multiplier method, judgment method 目 录引言 ………………………………………………………………………………………11.求解一个多元函数的条件...
