I'm new to M.V.T. and Rolle's Thm, so I guess I'm not quite comphrehending the concepts... Here's the problem:

Suppose that f is continuous on [0,4] and differentiable on (0,4). Also, suppose f(0)=1 and 3<f'(x)<6 for all x in (0,4). Which of the following must be true?

A) 13<f(4)<25

B) 3<f(4)<6

C) 12<f(4)<24

D) f(4) is undefined

Any help/explanation that would aid in my understanding of the concepts would be very appreciated!