The Height of a Hill (In Feet) Is Given By h

Multiple Choice

The height of a hill (in feet) is given by
$$h ( x , y ) = 30 \left( 14 - 5 x ^ { 2 } - 2 y ^ { 2 } + 3 x y + 30 x - 18 y \right)$$
where $x$ is the distance (in miles) east and $y$ is the distance (in miles) north of your cabin. If you are at a point on the hill 1 mile north and 1 mile east of your cabin, what is the rate of change of the height of the hill (a) in a northerly direction and (b) in an easterly direction?

A) (a) $570 \mathrm { ft } / \mathrm { mi }$ , (b) $690 \mathrm { ft } / \mathrm { mi }$
B) (a) $- 570 \mathrm { ft } / \mathrm { mi }$ , (b) $690 \mathrm { ft } / \mathrm { mi }$
C) (a) $690 \mathrm { ft } / \mathrm { mi }$ , (b) $570 \mathrm { ft } / \mathrm { mi }$
D) (a) $690 \mathrm { ft } / \mathrm { mi }$ , (b) $- 570 \mathrm { ft } / \mathrm { mi }$