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| . since the minimum value of is occurring, for 0 ≤ θ < 2π, when θ = , the minimum value of du f is −|∇f|, occurring when the direction of u is the direction of ∇f (assuming ∇f is not zero).