(a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, that is, in the direction of Vf(x). Let be the angle between Vf(x) and unit vector u. Then Duf IV cos 0 Since the minimum value of ---Select--- is 0≤8<2, when = = the minimum value of Duf is -IV, occurring when the direction of u is ---Select--- occurring, for the direction of Vf (assuming Vf is not zero). (b) Use the result of part (a) to find the direction in which the function f(x, y) = x²y = x²y decreases fastest at the point (3, -3).