(** * Mean value theorem *)

Lemma MVT_cor4:
forall (f df : R -> R) a eps,
(forall c, Rabs (c - a) <= eps -> is_derive f c (df c)) ->
forall b, (Rabs (b - a) <= eps) ->
exists c, f b - f a = df c * (b - a) /\ (Rabs (c - a) <= Rabs (b - a)).