Rolle's Theorem and Mean Value Theorem

This lecture covers Rolle's Theorem, which states that for a continuous function f on a closed interval [a, b] that is differentiable on the open interval (a, b), if f(a) = f(b), then there exists a point c in (a, b) where the derivative of f is zero. It also discusses the Mean Value Theorem, which asserts that for a function f that is continuous and differentiable on the interval [a, b], there exists a point c in (a, b) where the derivative of f at c is equal to the average rate of change of f over [a, b]. Various examples are provided to illustrate these theorems.