解析几何中的最值问题

On Extreme Value Problems in Analytic Geometry

解析几何是高中数学的重要内容,其主要特点是综合性强,在解题中几乎处处涉及函数与方程、不等式、三角等内容。因此,在教学中应重视对数学思想、方法进行归纳提炼,如方程思想、函数思想、参数思想、数形结合的思想、对称思想、整体思想等思想方法,达到优化解题思维、简化解题过程的目的。本文通过对一些典型例题的分析和解答,归纳了解析几何中常见的解决最值问题的思想方法,总结了解答典型例题的具体规律,并提供了一些常用的解题方法、技能与技巧。

Analytic geometry is an important part of mathematics for senior high school students, the main characteristic of which is highly comprehensive. When solving the related problems, we need to involve the knowledge of function, equation, inequation and trigonometry almost everywhere. Therefore, during the process of teaching, in order to optimize thinking of solution and simplify the process of solving mathematical problems, we should attach importance to sum up mathematical thinking and ways of solving mathematical problem, such as the concept of equation, function, parameter, number and shape integration, symmetry, entirety and so on. Through analysis and solution on a few typical examples, this article summarizes the most popular ways and thinking of solving the extreme value problems and concrete rules of solving typical problems, and provides some approaches and techniques of solving the problems in common use as well.