Chapter 13.6, Problem 80ES

On a certain mountain, the elevation $z$ above a point $\left(x,y\right)$ in an $xy\text{-plane}$ at sea level is $z=2000-0.02x^2-0.04y^2,$ where $x,y,\text{ and }z$ are in meters. The positive $x\text{-axis}$ points east, and the positive $y\text{-axis}$ north. A climber is at the point $\left(-20,5,1991\right).$

(a) If the climber uses a compass reading to walk due west, will she begin to ascend or descend?

(b) If the climber uses a compass reading to walk north-east, will she ascend or descend? At what rate?

(c) In what compass direction should the climber begin walking to travel a level path (two answers)?