At what angle above horizontal path in that direction begins

Question

Suppose you are climbing a hill whose shape is given by the equation z = 1000 -0.01x²-0.02y²,

Where x, y, z are measured in metres, and you are standing at a point with coordinates (50, 80, 847). 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) If you walk northwest, will you start to ascend or descend?

(c) In which direction is the slope largest? What is the value of this slope? At what angle above the horizontal does the path in that direction begin?

(d) In which horizontal direction should you move to maintain a height of 847 metres?