ON ELEMENTARY METHODS OF SOLVING EXTREMAL TASKS

Abstract

The article is devoted to the consideration of extremal tasks studied in the school mathematics course by various elementary methods (algebraic, geometric, analytical). The concept of an extremal tasks ( or task of extrema) is briefly given, it is noted that even in ancient times great scientists of the past were engaged in such tasks. It is interesting that in the school mathematics course comparatively less attention is paid to extremum tasks, and the existing tasks are mainly solved by the method of mathematical analysis based on the study of the function. In this regard, it is noted that there are extremum tasks of a wide range, the solution of which is most appropriately considered not by the method of mathematical analysis, but by the so-called elementary methods, which use a number of properties of standard ratios, and also apply various, sometimes non-standard techniques and methods. It is stated that these techniques and methods have not found their full reflection in the course of elementary mathematics, since there are no clearly developed methodological systems for their use. The article considers a number of specific methods for solving extremal tasks without using a derivative, including the method of standard inequalities, the method of importing auxiliary parameters, the method of conditional assumptions, the coordinate method, the method of auxiliary constructions, the linkage method and iteration method.