(** ** Definition and derivative of power function with natural number exponent *)

Definition pow_fct (n:nat) (y:R) : R := y ^ n.

Theorem deriv_maximum : forall f (a b c:R) (pr:derivable_pt f c), a < c -> c < b -> (forall x:R, a < x -> x < b -> f x <= f c) -> derive_pt f c pr = 0.