Show 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 θ be the angle between ∇f(x) and unit vector u. Then Du f = |∇f| Correct: Your answer is correct. . Since the minimum value of Correct: Your answer is correct. is occurring, for 0 ≤ θ < 2π, when θ = , the minimum value of Du f is −|∇f|, occurring when the direction of u is Correct: Your answer is correct. the direction of ∇f (assuming ∇f is not zero).