3. A hiker is walking on a mountain with height above the z = 0 plane...

 

 

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3. A hiker is walking on a mountain with height above the z = 0 plane given by z = f(x, y) = 8-xy. The positive x-axis points east and the positive y-axis points north, and the hiker starts from the point P(2,1,6). a. In what direction should the hiker proceed from P to ascend along the steepest path? What is the maximum rate of change of the path at P? b. Walking east from P, will the hiker start to ascend or descend? c. In what direction should the hiker walk from P to remain the same height? 3. A hiker is walking on a mountain with height above the z = 0 plane given by z = f(x, y) = 8-xy. The positive x-axis points east and the positive y-axis points north, and the hiker starts from the point P(2,1,6). a. In what direction should the hiker proceed from P to ascend along the steepest path? What is the maximum rate of change of the path at P? b. Walking east from P, will the hiker start to ascend or descend? c. In what direction should the hiker walk from P to remain the same height?

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To find the direction in which the hiker should walk to reach the peak of the mo... View the full answer