Find the volume of the largest rectangular box with edges parallel to the axes that c

Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid Hint: By symmetry, you can restrict your attention to the first octant (where http://webwork.math.ucdavis.edu/webw...2c3aedd151.png), and assume your volume has the form http://webwork.math.ucdavis.edu/webw...56249bf891.png. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume: