Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following rates: dx /dt = 1 m/sec, dy/ dt = -2 m/sec, dz /dt = 1 m/sec. Find the rates at which the box’s (a) volume, (b) surface area, and (c) diagonal length s = 2x2 + y2 + z2 are changing at the instant when x = 4, y = 3, and z =2.

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Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following rates: dx /dt = 1 m/sec, dy/ dt = -2 m/sec, dz /dt = 1 m/sec. Find the rates at which the box’s (a) volume, (b) surface area, and (c) diagonal length s = 2x2 + y2 + z2 are changing at the instant when x = 4, y = 3, and z =2.

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Step 1

To determine the rate at which the box’s (a) Volume, (b) Surface area and (c) diagonal length are changing.

Step 2

Given:

Step 3

Formula Used:

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