Verify Rolles Theorem for the given interval by checking (a) = (b) and then finding a value c in (a, b) such that '(c) =

Verify Rolle’s Theorem for the given interval by checking ƒ(a) = ƒ(b) and then finding a value c in (a, b) such that ƒ'(c) = 0.

THEOREM 4 Rolle's Theorem Assume that f is continuous on [a, b] and differen- tiable on (a, b). If f(a) = f(b), then there exists a number c between a and b such that f'(c) = 0.