ALGORITHM FOR FINDING EXTREME POINTS OF CERTAIN CURVES

Objective: Development of an algorithm for studying the extrema of a function in the polar coordinate system and its application for curve analysis. Theoretical Framework: The study of curves was developed on the basis of the general theoretical foundations of mathematics, geometric problems, and tasks from mechanics, physics, natural sciences, and engineering. In the modern world, the study of curves brings significant benefits to many fields, particularly in construction and mechanical engineering. Method: The main methods of research were analysis, synthesis and methods of mathematical analysis of the study using a derivative. Results and Discussion: The research indicates the peculiarities of the concept of extremum in different coordinate systems. The coordinates of the curve point in the Cartesian coordinate system are defined as a function of φ. The extremum of these functions correspond to the extremum of the Cartesian coordinate system of this curve relative to the axis of the abscissa and ordinate. Research implications: The paper presents an algorithm for the method of finding the extreme points of a curve in polar and Cartesian coordinate systems simultaneously. This allows you to find additional points for plotting curves using the analytical method. Originality/Value: The curves are investigated as the functions in the polar system of coordinates.