Rolle Theorem

Rolle Theorem

graph TD A[Rolle's Theorem] A --> B[Definition] B --> C["If a function f is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the interval (a, b) such that the derivative f'(c) = 0."] A --> D[Applications] D --> E[Calculus] D --> F[Physics] A --> G[Examples] G --> H[Example 1] G --> I[Example 2]