An explorative study on "Differentiation, Rolle's theorem, and the mean value theorem: In Vedic and modern methods

Abstract

This research investigates Rolle's Theorem and the Mean Value Theorem (MVT), proving both theorems and exploring the principles of differentiation. It further integrates Vedic mathematical techniques to simplify and enhance the understanding of these fundamental calculus concepts. The study establishes rigorous proofs for Rolle's Theorem and the MVT, provides practical examples illustrating their applications, and demonstrates how traditional Vedic methods can expedite calculations and offer alternative approaches to problem-solving. The integration of Vedic techniques with modern calculus not only streamlines computations but also enriches the conceptual grasp of these important theorems.