Suppose that you are climbing a hill whose shape is given by the equation z = 1000 - 0.01x2 - 0.02y2 and you are standing at a point with coordinates (60, 100, 764).
(a) In which direction should you proceed initially in order to reach the top of the hill fastest?
(b) If you climb in that direction, at what angle above the horizontal will you be climbing initially?