differentiation

Let a < b and f : [a, b] --> R be differentiable. If f0(a) < w < f0(b), then prove that there is c is belong to (a, b) such that f '(c) = w. Note f ' may not be continuous on [a, b].

(Hint:
Consider the case w = 0 first. Then also do the case w =/= 0.)