Find the volume of the largest rectangular box with faces parallel to the coordinate planes that can be inscribed in the ellipsoid
9x^2 + 36y^2 + 4z^2 = 36.

Question

Find the volume of the largest rectangular box with faces parallel to the coordinate planes that can be inscribed in the ellipsoid 
9x^2 + 36y^2 + 4z^2 = 36.

tkhunny · Answer

Would it be the same as 8 times the largest rectangular box that can be inscribed in the same parabolic section of just the first octant?  One vertex on the origin and the opposite vertex on the paraboloid?

tkhunny · Answer

In other words,

We need the maximum value of 8*x*y*z subject to the single constraint 9x^2 + 36y^2 + 4z^2 = 36

What do you know of LaGrange?

anonymous · Answer

Not much, though we have to know how to solve this using LaGrange Multipliers as well as another method.

tkhunny · Answer

Well, then... Tackle LaGrange and maybe learn something about "another method"?