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恒成立问题一直是中学数学的重要内容.它是函数、数列、不等式等内容交汇处的一个较为活跃的知识点,在近几年的高考试题中,越来越受到高考命题者的青睐,有时在同一套试题中甚至有几道这方面的题目.它涉及的知识面广,综合性强,同时由于数学语言的抽象性,如何从题目信息中提取可借用的知识模块常常是学生的一个难题.求解这类问题的方法比较多,本文结合一道经典例题介绍一些恒成立问题的常见解法.
Constantly established problem has always been an important part of high school mathematics.It is a more active knowledge point of functions, numbers, inequalities and other content interchange points, in recent years, college entrance examination papers, more and more subject to college entrance examination proposition of favor, and sometimes In the same set of questions, there are even several topics in this area.It involves a wide range of knowledge, comprehensive, and due to the abstraction of mathematical language, how to extract borrowable knowledge from the topic information module is often a problem for students There are many ways to solve this kind of problem, this article combined with a classic example to introduce some common solutions to the problem of constant establishment.