Abstract

Abstract: Тhe education of mathematical abilities and curiosity in students and students gifted in mathematics is important for the assimilation of all subjects. At the same time, the ability to use existing knowledge to solve mathematical problems of varying degrees of complexity develops their creative potential. This article deals with some problems of various contents concerning applications of derivatives, including extreme problems (maximum and minimum problems), problems solved using extreme properties, convexity and other properties of functions, as well as questions of proving various inequalities, methods for solving them.