Calculus help needed please

Question

Which of the following statements is/are true?

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 '(c) = 0.

III. If f(x) is differentiable at x = c, then f(x) is continuous at x = c.

 

Question options:

1)	I only
2)	II only
3)	I and III only
4)	I and II only

Answer 1

I. is true. There is a theorem that states this

II. looks like the mean value theorem but be careful. It would need to state that f is continuous on [a,b] and differentiable on (a,b). So II. is false.

III. is true.