# Directional Derivative and Gradient

Let $\nabla f(a)=v$ then $u\cdot v= \Vert u \Vert \Vert v \Vert \cos \theta$ and since $\Vert u \Vert =1$ we get that $\vert D_uf \vert$ reaches a maximum when $\cos \theta = \pm 1$ which happens iff $u = \lambda v$ for some $\lambda \in \mathbb{R}$