函数最值问题解法探讨 毕业论文精选.doc

本 科 毕 业 论 文 题 目 函数最值问题解法探讨 院 别 数学与信息科学学院 专 业 信息与计算科学 指导教师 评阅教师 班 级 2008级4班 姓 名 学 号 2012年5月12日 目 录 摘要·······································································Ⅰ Abstract·····························································Ⅰ 1引言······································································1 2求函数最值的几种解法探讨···········································1 2.1 判别式法·····························································1 2.2 配方法·······························································2 2.3 均值不等式法························································ 3 2.4 换元法······························································· 3 2.5 三角函数法·························································· 4 2.6 单调性法 ·····························································4 2.7 导数法······························································· 5 3求解函数最值时应注意的一些问题··································6 3.1注意定义域···························································6 3.2注意值域····························································· 6 3.3注意参变数的约束条件················································ 7 3.4注意对判别式的运用·················································· 7 3.5注意均值不等式的运用················································8 4函数最值在实际问题中的应用········································9 结束语····································································12 参考文献·································································13 摘 要：函数最值问题是数学领域中的重要研究内容.它不仅仅只在教学中解决一些数学问题，而且经常运用于解决实际问题.在工农业生产、经济管理和经济核算中，常常遇到一些解决在满足一定条件下怎样使产出最多、效益最高但投入最小等之类的问题.生活中也时常会见到求用料最省、效率最高、利润最大等问题.而这些生活和经济问题一般都可以转化为数学中的函数类问题来分析研究，进而转化为求函数最大（小）值的问题，即为函数的最值探讨，这尤其对研究实际问题的人们来说尤为重要.而函数最值问题的解法包括一元函数和多元函数，同时也有初等与高等解法之分.本文主要通过从初等解法方面对一元函数最值问题进行研究，探讨各种不同的求解方法，阐述函数最值问题研究的重要性，得到求解函