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恒成立问题是高考近几年考查的热点问题之一.其主要考查方式是与函数、方程、不等式、三角、数列等高中数学中的主干内容相结合,运用的往往是函数的单调性、基本不等式、导数等工具,最后一般归结为求函数最值问题、值域问题.一、恒成立问题的几种常见处理策略策略1构造函数,直接求函数最值例1不等式x~2-ax+1≥0在x∈R上恒成立,求a的范围分析可以看作二次函数f(x)=x~2-ax+1的最小值大于等于0.由于二次函数开口向上,在对称轴处取
One of the hottest questions in college entrance examination in recent years is the establishment of a permanent college entrance examination.The main way of examination is to combine the main contents of mathematics such as function, equation, inequality, trigonometry, Inequality, derivatives and other tools, the final generalized to find the value of the function of the most value problems, the value of the domain. A constant problem of several common strategies to deal with a constructor, seeking the most direct value of the function Example 1 inequality x ~ 2-ax + 1≥0 holds on x∈R, and the range analysis of a can be regarded as the quadratic function f (x) = the minimum value of x ~ 2-ax + 1 is greater than or equal to 0. Since the quadratic function opens upwards, Take the shaft