Suppose you are climbing a hill whose shape is given by the equation z = 2000 Acˆ' 0.005x2 Acˆ' 0.01y2,
where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1966). The positive x-axis points east and the positive y-axis points north.
(a) If you walk due south, will you start to ascend or descend?
(b) At what rate?
(c) If you walk northwest, will you start to ascend or descend?
(d) At what rate? (Round your answer to two decimal places.)
(e) In which direction is the slope largest?
(f) What is the rate of ascent in that direction?
(g) At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.)