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

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    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 ), and assume your volume has the form . Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume:
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    Quote Originally Posted by ewkimchi View Post
    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 ), and assume your volume has the form . Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume:
    Maximise V subject to the given constraint (the equation of the ellipsoid). Please show your work and say where you get stuck if you need more help.
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