Proof: let h() = [rb)-f(a)]t-[b-aro. (a b). then hiscontinuous onla bla is differentiable in (a, b), and ha) - fb)a-f(a)b h(b). to prove the theorem, we have to show that a co h(t) > h(a) for some t ? (a, b) , let x be a point on [a, b] at which h attains its maximum. then x e (a, b), and ) 0 if h ha) for some te la, b), the same argument applies if we choose for x a point on [a, b] where h attains its minimum 0 for some xe (a d1 if h is constant, this holds for every ? ? (a, b). if