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How do I approach this question?

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- Oct 29th 2009, 03:27 PMJohnLeeeDirectional Derivative and Gradient
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How do I approach this question?

Thanks - Oct 29th 2009, 05:23 PMJose27
Let $\displaystyle \nabla f(a)=v$ then $\displaystyle u\cdot v= \Vert u \Vert \Vert v \Vert \cos \theta$ and since $\displaystyle \Vert u \Vert =1$ we get that $\displaystyle \vert D_uf \vert$ reaches a maximum when $\displaystyle \cos \theta = \pm 1$ which happens iff $\displaystyle u = \lambda v$ for some $\displaystyle \lambda \in \mathbb{R}$