Suppose the elevation z above a point (x, y) in a horizontal xy- plane at sea level is z = 5cos (0.01(x? + y²)) meters. The positive x-axis points east, and the positive y-axis point north. A climber is at the point (6, 8, 2.70). If the climber uses a compass reading to walk southwest, will he ascend or descend? At what rate? Give your answer rounded to the nearest hundredth, and explain what the units are.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.