Методологія застосування похідних для знаходження оптимальних рішень в економічних та технічних системах

Abstract

This paper explores the role of the derivative as a fundamental optimisation tool in modern economic and technological systems. The relevance of the work stems from the need to improve the accuracy of management decisions in conditions of limited resources. The purpose of this study is to compare classical methods (Lagrange, CCT) with modern gradient-based approaches in machine learning. As a result, it was found that the effectiveness of the mathematical model depends directly on the correctness of the sensitivity analysis using partial derivatives. The results can be used to design intelligent decision support systems