Which of the following statements is/are true? If f '(x) exists and is nonzero for all x, then f(1) ≠ f(0).

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.

If f '(c) = 0, then f has a local maximum or minimum at x = c.