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Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one

Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane 3x + y + 4z = 9

1. volume = 3/4

2. volume = 9/8

3. volume = 27/4

4. volume = 9/4

5. volume = 9/2

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