Which of the following statements is/are true? I. If f'(x) exists and is nonzero for all x, then f(1) is not equal f(0). II.If f is differentiable for all x and f(-1) = f (1), then there is a number c, such that |c| < 1 and f'(c) = 0. III. If f'(c) = ), then f has a local maximum or minimum at x = c.
