Q: If $D_vf(a)=h^2+k^2$,Prove that $f$ is not differentiable on $a$ Assume that for $f:U\subseteq\mathbb R^2\to\mathbb R$ on the point $a\in U$ and in the direction $v=(h,k)$ we have:  $D_vf(a)=h^2+k^2$  
Prove that $f$ is not differentiable on $a$.  
My try:  
Assume that $f$ is differentiable on $a$.
So, we conclude that $Df(a)(v)=D_vf(a)=h^2+k^2$  
But, this doesn't reach a contradiction... That's where i'm stuck...

A: Hint: prove that, if $f$ is differentiable at $a$, then the map $v\mapsto D_v f(a)$ is linear.
