The height on the surface of the mountain is described by the h(x,y) = 4000 - .001 x2 - .004 y2 for each of the following parts assume that you are currently standing at the point on the surface corresponding to x = 500 y = 300.
a) How steep is the incline at this point if you are walking in the positive y direction?
b) At what rate is your height on the surface changing at this point if you are walking toward x = 400 y = 200?
c) In what (instantaneous) direction should you move in order to descend at the greatest rate?