We have teh equation, z = 1000 - 0.005x2 - 0.01y2
We need to strat by finding directional derivatives:
∂z/∂x = - 0.01x
Suppose you are climbing a hill whose shape is given by the equation z=1000-0.005x2-0.01y2, 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 largest? What is the rate of ascent in that direction? At what angle above the horizontal does the path in that direction begin?
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What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the 1D Relative Motion concept. If you need more 1D Relative Motion practice, you can also practice 1D Relative Motion practice problems.