THE APPLICATION OF DERIVATIVES IN PROVING INEQUALITIES - Sheraliev Sadulla Suyunboevich,; Djabbarov Odil Djuraevich, (INTEGRATION OF EDUCATION AND SCIENCE: GLOBAL CHALLENGES AND SOLUTIONS, 2026)
This paper explores the application of derivatives in proving mathematical inequalities. Derivatives serve as a fundamental tool in analyzing the behavior of functions, including their monotonicity and convexity, which are essential for establishing various inequality statements. The study presents theoretical foundations, key methodologies, and illustrative examples that demonstrate how derivative-based techniques can rigorously and effectively prove classical and modern inequalities. The results highlight the significance of derivatives in both pure and applied mathematics, offering a structured approach to inequality proofs that enhances understanding and facilitates further research.