Question

Which of the following statements is/are true? (5 points)
I. If f '(x) > 0 on (a, b), then f(x) is increasing on [a, b].
II. If f(a) = f(b), then there exists a number c in (a, b) such that f '(x) = 0.
III. If f(x) is differentiable at x = c, then f(x) is continuous at x = c.