Lemma MVT_abs : forall (f f' : R -> R) (a b : R), (forall c : R, Rmin a b <= c <= Rmax a b -> derivable_pt_lim f c (f' c)) -> exists c : R, Rabs (f b - f a) = Rabs (f' c) * Rabs (b - a) /\ Rmin a b <= c <= Rmax a b.