Suppose that f is continuous and differentiable on [a,b], f(a) = f(b) = 0. Show that for every real number $\displaystyle \lambda$ there is a real number c $\displaystyle \in$ [a,b] such that f'(c) = $\displaystyle \lambda$f(c).

Tried to use MVT (and Rolle's) to no avail. Any suggestions?