Mean Value Theorem for Continuous Functions

The Mean Value Theorem for Continuous Functions stands as a fundamental concept in calculus, playing a pivotal role in understanding the behavior of functions over a closed interval. Formulated by Augustin-Louis Cauchy, this theorem asserts the existence of a specific point within the interval where the instantaneous rate of change equals the average rate of change. Essential in bridging differential and integral calculus, the Mean Value Theorem provides a crucial analytical tool for studying the dynamics of continuous functions, forming a cornerstone for further exploration into the principles of mathematical analysis.