In order to develop students' thinking in mathematics and increase their interest in this subject,
you need to solve as many interesting or non-standard problems as possible. Non-traditional ways of solving nonstandard
problems are considered in this article. When solving the proposed problems, we use the knowledge gained
from the study of mathematical analysis. Before you start solving the problem, you need to remember the information
about the function and its properties. Which properties of the function should be used in solving various equations and
inequalities are considered in detail on specific examples. The monotonicity properties and extreme properties of the
function that are used in solving such problems are considered in this article.