ON THE METHOD OF SOLVING OF EXTREME PROBLEMS USING QUADRATIC FUNCTIONS

Abstract

In many cases, it is not always the case that the direct application of known methods of differential calculus is the best method for solving extremal problems. Sometimes it turns out that solving the problem with that method is simply impossible. Along with the emergence of the theory of modern extremal problems, mathematicians have to deal more and more often with not differentiable or discontinuous functions. On the other hand, meaningful problems for determining the extremal values of a function are not often found in elementary school mathematics textbooks and problem books.In this article, the possibility of using the extremal properties of the quadratic function in the field of solving optimized (improved) problems, without using the derivative, is presented in a way that is understandable to a student of a general education school. Some applied problems are considered in detail, with the solution of which it is justified that the extremal properties of the quadratic function not only allow to effectively and informally solve quite difficult extremal problems, but also significantly increase the level of students' motivation towards the study of mathematics.