Hello,

We are working on some multi-variable max/min problems in class but this question seems quite complicated. I tried messing around with it for a while but can't see how to get the answer. If anyone can help I would really appreciate it.

The question asks: Find the volume of the largest rectangular box (with faces parallel to the coordinate planes) that can be inscribed inside the ellipsoid

x^{2}/a^{2}+y^{2}/b^{2}+z^{2}/c^{2}=1