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Suppose that a mountain has the shape of an elliptic paraboloid , where a and c are constants, x and y are the east-west and north-south map coordinates and z is the altitude above the sea level (x,y,z are measured all in metres). At the point (1,1), in what direction is the altitude increasing most rapidly? If a marble were released at (1,1), in what direction would it begin to roll?
Gradients are investigated with respect to an Elliptic Paraboloid and Vector Fields. The solution is detailed and well presented.