Rolle’s theorem states: Suppose that y = f(x) is continuous at every point of the closed interval [a, b] and differentiable at every point in the open interval (a, b). If f(a) = f(b) then there is at least one number c in (a, b) where f'(c) = 0
Why is it important that the function be differentiable in the interval? What can happen if the function is not differentiable that might make the conclusion untrue?