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数学教学过程中,恒成立问题主要考查的是方程、不等式、函数等知识内容,与参数的取值范围和函数最值是具有紧密联系的。恒成立问题是高中数学教学的重点和难点,并且还是高考的考点,恒成立的解决方法主要有一次函数、二次函数、构造函数、分离参数和数形结合还有更主元法。在近几年的高考试题中经常遇到不等式恒成立的问题,由于高中教材对不等式恒成立的问题只是稍微提及,导致学生无法找到问题切入口从而无法解题。然而这类问题可以利用函数的特殊值和单调性来解决,采用变量分离法等多个解法进行。
In the process of mathematics teaching, the main problems of the founding of constant are the contents of equations, inequalities, functions and other knowledge, which are closely related to the range of values of the parameters and the value of the function. Constantly established problem is the key and difficult point of high school mathematics teaching, and is still the entrance examination, the establishment of permanent solutions are mainly a function, quadratic function, constructor, the separation of parameters and the number of forms there is a more primary method. In recent years, college entrance examination questions often encounter the inequality of the establishment of the problem, due to inequality of high school teaching materials established the problem is only mentioned a little, resulting in students can not find the problem cut the entrance and thus can not solve the problem. However, this kind of problem can be solved by using the special value and monotonicity of the function, adopting multiple solutions such as variable separation method.