Suppose you are walking on a terrain for which elevation $($in feet$)$ is modeled by the function

f$($x$,$y$)=2000-0\mathrm{.}01$x$^(2)-0\mathrm{.}04$y$^(2)$

where the positive x axis points east and the positive y axis points north.

$($a$)$ Make a contour plot of the elevation function by drawing level curves for the following

values: $1600,1900,$ and $2000.$

$($b$)$ You are standing at the point $(100,50)$ on the xy map of the terrain plotted in $($a$).$

What is the elevation at your current position? How far away are you from the summit?

$($c$)$ If you start walking north from your position, will your elevation increase or decrease?

At what rate?

$($d$)$ If you start walking southwest from you position, will your elevation increase or de$-$

crease? At what rate?

$($e$)$ What direction do you need to go in order to climb the steepest slope from your current

location?

$($f$)$ Suppose you decide to go straight to the summit from your current position $($i$.$e$.$ cor$-$

responding to a straight line on the map$).$ At what rate will your elevation increase or

decrease?