I am having a bit of trouble setting up a problem:

(1) Find the volume of the largest regtangular box with edges parallel to the axes that can be inscribed in the ellipsoid: 9x^2 + 36y^2 + 4z^2 = 36

I thought it would be simply:

f(x,y,z) = xyz && g(x,y,z) = 9x^2 + 36y^2 + 4z^2 = 36

However, this seems to give me the wrong solution.

Any help would be appreciated.