(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 = |vf|| cos 0 ✓ Since the minimum value of cos 0 is -1 occurring, for 0 ≤ 0 < 2л, when = π the minimum value of Duf is -|Vfl, occurring when the direction of u is the opposite of v Vf is not zero). the direction of Vf (assuming - (b) Use the result of part (a) to find the direction in which the function f(x, y) = x²y − x²y³ decreases fastest at the point (5, -1). (810, 1053) Need Help? Read It Watch It

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