Suppose that V is convex and open in Rn and that f: V → Rn is differentiable on V. If there exists an a ∈ V such that Df(x) = Df(a) for all x ∈ V, prove that there exist a linear function S ∈ £(Rn; Rn) and a vector c ∈ Rn such that f(x) = S(x) + c for all x ∈ V.