Formation of the skill to solve extremal problems in the school course of mathematics.

The article is devoted to extremal problems of the school mathematics course. The authors build two separate lines in the discussion of the stated topic, dividing various methods for solving extremal problems into methods that implement algebraic and geometric approaches. In the case of applying the first of them, the solution (of both algebraic and geometric problems) is consistent with the stages of mathematical modeling. For the case of applying the second of them, the work focuses on the so-called basic method. With its help, the solution of the first extremal problems of geometry is realized, reliance on it is carried out in the process of solving the discussed problems using other geometric methods. The authors highlight the sequence of actions as part of the basic method. Within the framework of each line of discussion, the preparatory work carried out in anticipation of solving extremal problems by various methods is characterized.