$2.($TM $1-40$; $5$ pts total$)$ The height of a hill in meters is given by z $2$xy $3$x$24$y$218$x $`$

$28$y $`12,$ where x is the distance east and y is the distance north of the origin.

$($a$)(1$ pt$)$ Where is the top of the hill?

$($b$)(1$ pt$)$ What is the elevation at the peak?

$($c$)(1$ pt$)$ How steep is the hill at x $$ y $1,$ that is$,$ what is the angle between a vector

perpendicular to the hill and the z axis?

$($d$)(2$ pts$)$ In which compass direction is the slope at x $$ y $1$ the steepest?