(Solution) - The height of a certain hill in feet is given -(2025 Original AI-Free Solution)

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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?