Exercise 30

Near a buoy, the depth of a lake at the point with coordinates \((x, y)\) is \(z = 200 + 0.02x^2 - 0.001y^3\), where x, y, and z are measured in meters. A fisherman in a small boat starts at the point \((80, 60)\) and moves toward the buoy, which is located at \((0, 0)\). Is the water under the boat getting deeper or shallower when he departs? Explain.