(a) Assume both : R + R2 and f: R2 + R are differentiable with a (0) = (0,0) and f(0,0) = 0. Use chain rule to show that g(t) = f(at)) is differentiable at t = 0 and g'(0) = V f(0,0) a' (0). (b) Let my? 22+y2 f(x, y) { if (x,y) (0,0) if (x, y) = (0,0) 0 Show that af/ax and af/ax both exist at (0,0). Is f differentiable at (0,0)? ab2 but V f(0,0) - '(0) = 0. (C) Let (t) = (at, bt) for constants a and b. Let f(x, y) be as in part (b). Show that g(t) = f(a(t)) is differentiable at 0, g'(0) Explain why this does not contradict with part (a). a2 +62