Question

Which of the following statements is/are true?

If f '(x) > 0 on (a, b), then f(x) is increasing on [a, b].
If f(a) = f(b), then there exists a number c in (a, b) such that f '(x) = 0.
If f(x) is differentiable at x = c, then f(x) is continuous at x = c.
I only
II only
I and III only
I and II only

Answer 1

c) I and III only

THird one is true and it is only option containing the third option