largest box with edges that can be inscribed into the ellipsoid
I again used the larange multiplier using v=8xyz and my g function.
Dear JaneP.,
I do not like the Langrange multiplication method, so I suggest you to stay at the elementary way: from constraint(now the equation of the ellipsoid) we express one of the variations and substitute into V function.So we get a two-variant function, we can find the maximum with the usage of derivation.
Trick: use V^2 insteed V so you don't get square root.
Hello, JaneP!
Largest box with edges that can be inscribed into the ellipsoid
I again used the Larange multiplier using and my function.
. . Due to the symmetry, we can work in the first octant, so that:
We have: .
Equate the partial derivatives to zero . . .
. .
From [1], we have: .
From [2], we have: .
From [3], we have: .
Equate [4] and [5]: .
Equate [4] and [6]: .
Substitute [7] and [8] into [4]: .
. .
Therefore: .