Suppose that you are climbing a hill given by the equation: x^2 + y^2 - 6x +z = 0

a/ Your route is such that as you pass through the point P(1,1,4) you are heading northeast. At what rate (with respect to distance in meters) is your altitude changing at that point?

b/ Your partner at Q(1,2,1) wants to start upward as quickly as possible. In what direction should she take off? At what rate (with respect to distance in meters) is her altitude changing when she starts?