Let f : [0, 1] - R be a continuous function such that f(0)

Let f : [0, I] IR be a continuous function such that f(0) < f(l). By considering the function f(c) f(l) f(0) - f(l) or otherwise, prove that there exists c e [0, I] such that f(c) f(l) = (f(0) f(l))c.