The function h is continuous on the closed interval [3,9] with h(3) = 1 and h(9) = 4. Of the following conditions, which would guarantee that there is a number c in the open interval (3,9) where h'(c) = 1/2?

A) h has a minimum value on the closed interval [3,9].
B) h is increasing on the closed interval [3,9].
C) The graph of h has at least one horizontal tangent in the open interval (3,9)
D) h is differentiable on the open interval (3,9)
E) None of the above.