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恒成立问题是高中数学中的一个热点,而不等式更是高考的重点,有人说“不等式恒成立问题”是高考的兴奋点,这不无道理.这类问题的解决涉及一次函数、二次函数、三角函数、指数与对数函数等函数的性质、图像,渗透着换元、化归、数形结合、函数与方程等思想方法,有利于考查学生的综合解题能力,在培养思维的灵活性、创造性等方面起到了积极的作用.由于此类问题解法灵活、综合性强,部分考生常感到无从下手,茫然不知所措,那么到底如何解决这类问题呢?
The problem of constant establishment is a hot topic in high school mathematics. The inequality is the focus of the college entrance examination. Some people say that the “inequality constant establishment problem” is the excitement point of the college entrance examination. This is not without reason. The solution of such problems involves a function, two The functions and functions of functions such as subfunctions, trigonometric functions, exponentials, and logarithmic functions, permeate such ideological methods as substitution, transformation, combination of numbers, functions, and equations, which are beneficial to students’ comprehensive problem-solving abilities. The flexibility, creativity and other aspects have played a positive role. Due to the flexible and comprehensive solution of such problems, some candidates often feel at a loss and are overwhelmed, so how to solve such problems?