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不等式恒成立问题是中学数学的一类重要题型,它散见于许多知识板块中,载体较多,而且不少情况下题意较为隐含。正因为其涉及内容较广、表现形式多样、思维层次较高,因而倍受高考命题者的青睐。概括一下,不等式恒成立问题主要涉及到一次函数、二次函数的性质、图像,导数、不等式等数学知识,渗透着换元、化归、数形结合、函数与方程等思想方法。解答这类题目主要有四种方法:其一,利用一次函数单调性;其二,利用二次函数单调性;其三,分离参数、转化为求函数最值(或上、下界);其四,利用数形结合法。下面简单地谈一谈恒成立问题的常见类型及其解题策略。
Inequality constant problem is the establishment of an important class of high school mathematics questions, which scattered in many knowledge plate, the carrier more, and in many cases the meaning is more implied. It is because of its wide range of content, diverse forms of expression, higher level of thinking, and thus highly acclaimed college entrance examination proponents of all ages. To summarize, the problem of establishing inequalities mainly involves such mathematical methods as the nature of first order functions, quadratic functions, images, derivatives, inequalities and other mathematical methods, which permeate the thinking methods of commutation, regression, combination of numbers, functions and equations. There are mainly four ways to answer such questions: one is to use the monotonicity of the first-order function; the second is to make use of the monotonicity of the second-order function; the third is to separate the parameters into the most value (or upper and lower bounds) of the function; , The use of digital combination method. The following briefly talk about the common types of constant problems and the problem-solving strategy.