Let $f(x,y)=x+y^2$ and $P = (1,1)$. Find a unit vector $u$ such that the directional derivative $D_uf(x,y)$ is zero.
$ \nabla{f(x,y)} = \left\langle1, 2y\right\rangle\\ \nabla{f(1,1)} = \left\langle11, 2\right\rangle\\ D_uf(1,1) = \left\langle11,2\right\rangle\cdot u\\ $
$u$ must be a unit vector so $u = \sqrt{x^2+y^2} = 1$. So we must solve the system of equations:
$ \sqrt{x^2+y^2} = 1\\ x + 2y = 0 $
Then we simply solve the system of equations. Is this the correct direction for this problem?