Applications Of The Theory Of Extrema To Practical Problems

Abstract

This paper explores the applications of the theory of extrema to solving practical problems. A number of applied problems from mechanics, geometry, physics, and engineering are analyzed using methods of mathematical analysis. For each problem, an appropriate mathematical model is constructed, and optimal solutions are obtained by determining the maxima and minima of single-variable functions. Critical points are identified using firstand second-order derivatives. The results demonstrate that the theory of extrema is a universal and effective tool for optimizing real-world processes and plays an important role in integrating theory and practice in teaching mathematical analysis