数学分析研究论文.doc

中国某某大学(本科)
数学分析研究论文
数信小组

题目:函数的极值和最值的研究
学院:数学与计算科学学院
年级:2011级
指导老师:X X(教授)
完成时间:2014年6月8日
函数极值与最值研究
摘要:在实际问题中, ,以及二元以上的多元函数的最值问题和极值问题等诸多函数常见问题。求一元函数的极值,主要方法有:均值等式法,配方法,求导法等。求一元函数的最值,主要方法有:函数的单调性法,配方法,判别式法,复数法,导数法,换元法等。求二元函数极值,主要方法有:条件极值拉格朗日乘数法,偏导数法等。求二元函数最值,主要方法有:均值不等式法,换元法,偏导数法等。对于多元函数,由于自变量个数的增加, 从而使该问题更具复杂性,求多元函数极值方法主要有:条件极值拉格朗日法, 等,:向量法,均值不等式法,换元法,消元法,柯西不等式法,数形结合法等,
关键词:函数,极值,最值,极值点,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 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 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 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, bination method,
Keywords: function, extreme value, the value, extreme points, methods and techniques
引言
作为函数性质的一个重要分支和基本工具,函数极值和最值在数学与其他科学领域,如数学建模优化问题、概率统计等学科都有广泛应用。
不仅如此,函数极值理论在航海、保险价格策划、航空航天等众领域中也是最富变现性和灵和性,并起着不可替代的数学工具作用,许多实际问题最终都归结为函数极值和最值问题,生活中遇