Let C c RN such that for all a, b e C there exists a differentiable function g: [0, 1] → C such that g(0) = a, g(1) = b. Let f: C - R be differentiable. a) Let x, y e C. Show that there exists z € C such that f(y)-f(x) = (Vf(z), y - x) b) Show that f is constant if and only if Vf(x) = 0 for all x e C.