how that a differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, that is, in the direction of ??f(x). Let ? be the angle between ?f(x) and unit vector u. Then Du?f = |?f| . Since the minimum value of is occurring, for 0 ? ? < 2?, when ? = , the minimum value of Du?f is ?|?f|, occurring when the direction of u is the direction of ?f (assuming ?f is not zero). (b) Use the result of part (a) to find the direction in which the function f(x, y) = x4y ? x2y4 decreases fastest at the point (3, ?3).