解析几何中的最值问题研究
学 生：李 霞
指导教师：任全红
摘 要：解析几何中的最值问题具有综合性强、涉及知识面广而且常含有变量的一类难题，也是数学中的一个难点.解决这类问题往往利用函数与方程思想、数形结合思想、转化与化归等数学思想方法，将其转化为解不等式或求函数值域，以及利用函数单调性、建立几何模型的思想来解决.本文就通过具体问题分析，对解析几何中常见的最值问题进行系统研究.我们首先通过对解析几何中最常见的几类最值问题进行研究，我们找到了一些解最值问题最常用的方法，然后我们通过进一步的观察总结又找到了解最值问题的特殊方法.
关键词：解析几何；最值问题；函数
The Study of the Extreme Value in Analytic Geometry
By Li Xia
Guided by Ren Quanhong
Abstract : The extreme value in Analytic geometry is a kind of difficulty in math study because of its strong comprehension ,vivid knowledge and usual varieties . To solve this problem , inequalities and the value of field of function should be found under the methods of combination of numbers and shapes , the construction of models or the monotonicity of function and so on . This paper is to
make a systematic study on the extreme value according to a series of specific analysis . Firstly the common methods could be gotten after analyzing some different fields of this problem, and then the special solutions after further observation.
Key words :analytic geometry; the extreme value; the function
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