4. Consider a curve (t) = (t, t, 2t - 1) and a function f : R R given by f(x, y, z) = (x+y, 2yz, 3x y + z = 4). (a) What is the tangent vector u to the curve at t = 2? (b) Calculate the differential df. (c) What is the tangent vector to the image curve f(y(t)) at t = 2? (d) Calculate df (u). What do you notice? (e) Assume that this property generalizes to arbitrary and f (it does). In words, how would you describe this property?