calculus simple question?

Question

f is continuous on [0,4] and differentiable on (0,4). Also, suppose f(0) =1
and 3 a. 13 b. 3 c. 12 d. undefined

Answer 1

By the mean value theorem, there exists an a in (0,4) such that f(4) = f(0) +(4 -0) f'(a) = 1 + 4 f'(a). Since 3
1 + 4*3 < f(4) < 1 + 4*6, or
13 < f(4) < 25 (a)

Answer 2

b. 3

you silly sausage