Can somebody please help I do not know how to do this and have an exam tommorow!

Suppose that f : [a; b] --> R is a differentiable function, and assume f'(a) <

k < f'(b). Show that there exists c in (a; b) with f'(c) = k. Do NOT assume that f' is

continuous! Hint: consider g(x) = f(x) - kx.