Question: Find the dimensions of the rectangular box with maximum volume in the first octant with one vertex at the origin and the opposite vertex

Find the dimensions of the rectangular box with maximum volume in the

Find the dimensions of the rectangular box with maximum volume in the first octant with one vertex at the origin and the opposite vertex on the ellipsoid 4x2 + 4y? + z? = 4. The length of the box in the x-direction is. (Type an exact answer, using radicals as needed.) The width of the box in the y-direction is (Type an exact answer, using radicals as needed.) The height of the box in the z-direction is (Type an exact answer, using radicals as needed.)

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