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高中数学中的恒成立问题,涉及到一次函数、二次函数、指数函数、对数函数的性质、图象,渗透着换元、化归、数形结合、函数与方程等思想方法,在培养思维的灵活性、创造性等方面起到了积极的作用。因此也成为历年高考的一个热点。恒成立问题在解题过程中大致可分为以下几种类型:①一次函数型;②二次函数型;③指数、对数型;④三角函数型等。解法通常使用:①数形结合法;②函数最值法;③变量分离法。
The establishment of permanent mathematics in high school mathematics involves the functions and functions of primary function, quadratic function, exponential function, logarithmic function, permeation such as substitution, transformation, combination of number and shape, function and equation, and so on. The flexibility and creativity of thinking have played an active role. Therefore, it has become a hot spot in the college entrance examination over the years. Constant establishment problems can be roughly divided into the following types in the course of solving problems: 1 function of a type; 2 functions of a quadratic function; 3 types of an exponential, logarithmic; and 4 types of trigonometric functions. The solution method usually uses: 1 number form combination method; 2 function maximum value method; 3 variable separation method.