Derivative is widely used in functions, which can judge the monotonicity of functions, the extreme value and point of functions, the maximum (minimum) value of functions in a certain interval, the concavity and convexity of functions, inflection points and so on. Derivative is an effective tool for us to analyze and solve problems. Derivative (abbreviation of derivative function) is the foundation of modern mathematics and one of the most important basic concepts in mathematics teaching. Derivative is the link between elementary mathematics and advanced mathematics. Derivation and definition of derivative always run through the idea of function, which is a special function and plays a very important role in the application of function.

The application of derivative in function mainly includes:

Judging the monotonicity of the function;

Find the extreme value and extreme point of the function;

Find the maximum and minimum value of the function;

Judge the concavity and convexity of the function and find the inflection point of the function.