The height of a certain hill (in feet) is given by
$h(x, y) = 10(2xy − 3x^2 − 4y^2 − 18x + 28y + 12)$,
where $y$ is the distance (in miles) north, $x$ the distance (in miles) east of South Hadley.
How steep is the slope at $y=1$, $x=1$?
My thoughts:
The directional derivative is given by $\nabla h(1, 1)\cdot\mathbf{u}$, where $\mathbf{u}$ is a unit vector. But what do I take as $\mathbf u$?