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

question 84

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 ft/mi, (b) 690 ft/mi
• B) (a) -570 ft/mi, (b) 690 ft/mi
• C) (a) 690 ft/mi, (b) 570 ft/mi
• D) (a) 690 ft/mi, (b) -570 ft/mi

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