數(shù)學(xué)分析研究論文(已修改)
2025-08-17 07:24 本頁(yè)面
【正文】 中 國(guó) 某 某 大 學(xué)(本科) 數(shù)學(xué)分析研究論文 數(shù)信小組 題 目:函數(shù)的極值和最值的研究 學(xué) 院:數(shù)學(xué)與計(jì)算科學(xué)學(xué)院 年 級(jí):2011級(jí) 指導(dǎo)老師:X X(教授) 完成時(shí)間:2014年6月8日函數(shù)極值與最值研究 摘要：在實(shí)際問題中,，以及二元以上的多元函數(shù)的最值問題和極值問題等諸多函數(shù)常見問題。求一元函數(shù)的極值，主要方法有:均值等式法，配方法，求導(dǎo)法等。求一元函數(shù)的最值，主要方法有:函數(shù)的單調(diào)性法，配方法，判別式法，復(fù)數(shù)法，導(dǎo)數(shù)法，換元法等。求二元函數(shù)極值，主要方法有：條件極值拉格朗日乘數(shù)法，偏導(dǎo)數(shù)法等。求二元函數(shù)最值，主要方法有:均值不等式法，換元法，偏導(dǎo)數(shù)法等。對(duì)于多元函數(shù)，由于自變量個(gè)數(shù)的增加,從而使該問題更具復(fù)雜性，求多元函數(shù)極值方法主要有：條件極值拉格朗日法,等，：向量法，均值不等式法，換元法，消元法，柯西不等式法，數(shù)形結(jié)合法等， 關(guān)鍵詞：函數(shù)，極值，最值，極值點(diǎn),方法技巧． Abstract: in practical problems,often encounter a unary function. The function of two variables, and multiplefunctions of two yuan more than the most value questionand extremum problems and many other functions of mon problems. Extremum seeking a binary function,the main methods are: inequality extremum method,distribution method, derivation etc.. The value for theelement function, the main methods are: monotone method, function method, the discriminant method,plex method, derivative method, substitution methodetc.. For two yuan value function, the main methods are:conditional extremum of Lagrange multiplier method etc..Ask two yuan to the value function, the main methods are:mean inequality method, substitution method, partial derivative method etc.. For multivariate function, due to the increased number of variables,so that the more plicated the problem, find the function extreme value method mainly has: conditional extremum of multivariate Lagrange method, directional derivative, for multivariate function most value the most value problem with the function of one variable can be used to find the function extreme value is similar. The main methods are: vector method, the mean value inequality method, substitution, elimination method, the method of Cauchy inequality, the bination method,Keywords: function, extreme value, the value, extreme points, methods
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