函数最值问题的求解方法和应用初稿.doc

摘 要 函数最值问题是重要的分析问题之一。它不仅在教学中解决一些数学问题，而且常运用于解决实际问题.本文探讨了求函数的最值的几种解法，着重介绍了初等数学中的求函数方程的基本解法：判别式法、配方法、均值不等式法、换元法、向量法、单调性法、数形结合法、待定系数法和高等数学中函数方程的解法：导数法、函数的有界性法,同时介绍了求解函数最值时应注意的一些问题，在实际问题的应用过程中不断地熟练掌握这些解法,进一步阐述函数最值问题研究的重要性。 关键词：函数最值，初等数学, 高等数学，导数 ABSTRACT The function of extremum is one of the important problems of analysis. It not only in the teaching solving mathematical problems, and often used in solving practical problems. This paper discusses the solution of the function of extremum, introduces the basic method to solve the function equation in Elementary Mathematics:Discrimi- nant analysis method,completing square,the mean value inequality method,method of substitution,vector method,the monotony of function method,combining numbers with shapes method,method of undetermined coefficients,and solution of equations in Higher Mathematics:derivative method,function boundedness method.At the same time, the solution of the value function and some problems should be paid attention to,In order to make full use of these solutions,further illustrates the importance of the value of a function. Keywords: most value of function; elementary mathematics; advanced mathematics; derivative 目 录 1引言······································································ 2求函数最值的几种解法················································ 2.1 判别式法····························································· 2.2 配方法······························································· 2.3 均值不等式法························································ 2.4 换元法······························································· 2.5 向量法································································ 2.6 单调性法 ····························································· 2.7 导数法······························································· 2.8 函数的有界性法······················································ 2.9 数形结合法··························································· 3求解函数最值时应注意的一些问题