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 ](adsbygoogle = window.adsbygoogle || []).push({});

I realize that the volume of the box: V = (2x)(2y)(2z) = 8xyz

Thus far I've solved for z^2 in the equation of the ellipsoid and then squared the volume so that I could make the substitution easier

V^2 = 64(x^2)(y^2)(9-24x^2-y^2)

Then I've taken the partial derivates of this to look cor critical points, but here I get an algebraic nightmare and can't find critical points. I'm wondering if my initial steps are correct, it's the only thing I could think of doing.

Any help would be great. thank you

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Optimization greatest possible volume Problem

**Physics Forums | Science Articles, Homework Help, Discussion**