Rolle’s and Mean value theorem

In this calculus lesson, Rolle’s and Mean Value Theorems are crucial for understanding how functions behave and finding specific points where important properties hold true. Rolle’s Theorem guarantees a point in a given interval where the tangent line is horizontal (derivative equals zero), while the Mean Value Theorem ensures a point where the instantaneous rate of change matches the average rate of change within any interval. By studying these theorems, you will gain a solid understanding of their practical applications in calculus, identify situations where they can be used, and uncover essential properties of functions.