Which of the following statements is/are true?

Question

I.If f '(c) = 0, then f has a local maximum or minimum at x = c.
II.If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].
III.The Mean Value Theorem can be applied to f(x) = 1/x^2 on the interval [-1, 1].

I only
II only
I and III only
I and II only

Answer 1

iii cannot be true at x=0 The function is not continous, which is a requirement for the MVT.

Answer 2

So would that mean that it is only the first one?