Prompt: Find points where the fastest change of the function $\displaystyle f(x,y) = x^2 + y^2 + x - 2y$ is in the direction of $\displaystyle \vec{v}=<1,2>$.

I'm hoping to get a few pointers on what to do here.

So far, my strategy is to find the directional derivative of $\displaystyle f(x,y)$ in the direction of $\displaystyle \vec{v}$.

$\displaystyle D_{u}f(x,y) = \triangledown f(x,y)\cdot\vec{u}$, where $\displaystyle \vec{u}$ is the unit vector of $\displaystyle \vec{v}$.

Could someone verify if this is the right path, otherwise, I would appreciate just a few hints on what to do here.