Suppose you are climbing a hill whose shape is given by the equation

z = 1000 - 0.005x^2 -0.01y^2, where x,y,z are measured in meters, and you are standing at a point with coorindates (60,40,966). The positive x-axis points east and the positve y axis points north.

a. if you are walk due south, will you start to ascend or descend? At what rate?

b. if you are walk northwest, will you start to ascend or descend? At what rate?

c. in which direction is the slope largest? What is the rate of ascent in that direction? At what angle above the horizontal does the path in that direction begin?

Any help is greatly appreaciated!!!!!!