Application of 1. derivative in judging monotonicity and maximum value of function

The general steps of finding the maximum value of a function by derivative are as follows: (1) First, find the derivative of the function according to the derivative formula; (2) Solving the independent variable that makes the derivative of the function equal to 0; (3) The monotone interval of the function is obtained from the derivative property; (4) Find the maximum value of the function from the monotone interval through the definition domain.

2. The application of derivative in function extremum.

Using the knowledge of derivative to find the extreme value of function is a common type of problem in high school mathematics. The general steps of finding the extreme value of a function by derivative are as follows: (1) First, find the derivative of the function according to the derivative rule; (2) Make the derivative of the function equal to 0, so as to find the zero point of the derivative function; (3) Starting from the number of zeros of the derivative function, the partition is discussed, and the monotone interval of the function is obtained; (4) Judge the extreme point of the function according to the definition of the extreme point, and finally find the extreme value of the function.

3. The application of derivative in finding the parameter range.

Using derivative to find the range of some parameters in the function has become a hot spot in the college entrance examination in recent years. In the general function problem with parameters, the range of parameters can be found more quickly by simplifying the function with derivatives.