Question

Suppose, that after work you are going for a trip and you are climbing a hill whose shape is given by the equation: z=1000-0.005x^(2)-0.001y^(2) where x,y, and z are measured in meters, and you are standing at a point with coordinates (60,40,966). 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? At what rate? b)if you walk northwest,will you start to ascend or descend? At what rate? c)in which direction is the slope the largest? d)what is the rate of ascend in that direction? e)at what angle above the horizontal does the path in that direction begin?

Answer 1