3. 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 is the distance (in miles)
east of the village.
(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 the village? In what direction is the slope
steepest at that point?
The Attempt at a Solution
I would think that I would have to use the derivative test to get the extrema and go from there, but we didn't cover that material yet. How else can I approach this?