The height of a certain hill (in feet) is given by

h ( x , y ) = 10(2xy − 3x2 − 4y2 − 18x + 28y + 12),

where y is the distance (in miles) north, x the distance east of South Hadley.

(a) Where is the top of the hill located?

(b) How high is the hill?

(c) How steep is the slope (in feet per mile) at a point 1 mile north and one mile east of South Hadley? In what direction is the slope steepest, at that point?

a.)

Step 1 of 3</p>

We have to find the location of the top of the hill.

The location of the top of the hill can be found by solving the expression,

The height (in feet) of the certain hill is given by,

where is the distance (in miles) north,

the distance east of South Hadley.

Substituting for in

Solve above two equations to get the values of and ,

Therefore, the top of the hill is located at 3 miles north, 2 miles west of South Hadley.

b.)

Step 2 of 3</p>

We have to find the height of the hill.

The height of the hill can be found by substituting as -2 and as 3 in the expression for h,

Therefore,

feet

Therefore, the height of the hill is 720 feet.

c.)