The seven basic inequalities for postgraduate entrance examination are partial inequality, inequality, mean inequality, functional inequality, inequality proof problem, basic inequality and inequality of linear algebra, which are proved by monotonicity of functions.

As the application of differentiation, the problem of inequality proof often appears in the postgraduate entrance examination questions. Using monotonicity of function to prove inequality is the basic method of inequality proof, and sometimes it needs to be used twice or even three times in succession. Other methods can be used as a supplement to this method, and the construction of auxiliary functions is still the key to solve the problem.

This inequality is proved by Lagrange mean value theorem. For the factors containing fa in inequality, we can consider using Lagrange mean value theorem to deal with them first.

Taylor formula is used to prove inequality. If the inequality to be proved contains the second or more derivative of the function, Taylor formula is generally used to prove inequality. The difficulty in proving inequality is also the construction of auxiliary function. Generally, the auxiliary function to be constructed can be obtained by analyzing the inequality to be proved.

Formulas that use symbols > and< to indicate the size relationship are called inequalities, and formulas that use ≠ to indicate inequalities are also inequalities. Constructing appropriate auxiliary function is the basis to solve the problem. Sometimes it is necessary to use the monotonicity of the function to prove the inequality twice, and sometimes it is necessary to divide the interval (A, B) and discuss it between cells respectively.