Question: [ A rectangular box, whose edges are parallel to the coordinate axes, is inscribed in the ellipsoid 96x^2 + 4y^2 + 4z^2 = 36, What is the greatest possible volume for such a box ]
I realize that the volume of the box: V = (2x)(2y)(2z) = 8xyz
Thus far I've solved for z^2 in the...