Question: Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoidx281+y249+z24=1x,y,z0V=8xyz. Then arguing bysymmetry, you

Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoidx281+y249+z24=1x,y,z0V=8xyz. Then arguing bysymmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume:

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