1. ## Multivariable calculus

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

I'm hoping to get a few pointers on what to do here.
So far, my strategy is to find the directional derivative of $f(x,y)$ in the direction of $\vec{v}$.

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

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

2. ## Re: Multivariable calculus

Not totally clear on the question, but I'll give it a shot.

The gradient of the function is $\triangledown f = (2x + 1) u_{x} + (2y - 2) u_{y}$

Since you want to find the point(s) where this function is the greatest, doesn't this mean it has to be differentiated again and then set to 0?