The surface of mountain is modeled by the equation h(x,y)=5000 -0.001x^2-0.004y^2. A mountain climber is at the point (500, 300, 4390). In what direction should the climber move in order to ascend at the greatest rates ? Give direction as a vector only i & j components needed.

From that, give the direction that climber should move so that his altitude does not change (h doesn't change). The climber is still assumed to be at the point (500,300,4390).