The height of a hill in meters is given by z = 2xy – 3x2 – 4y2 – 18x + 28y + 12, where x is the distance east and y is the distance north of the origin.
(a) Where is the top of the hill and how high is it?
(b) How steep is the hill at x = y 1, that is, what is the angle between a vector perpendicular to the hill and the z axis?
(c) In which compass direction is the slope at x = y = 1 steepest?