A rectangular box is to be inscribed inside the ellipsoid #2x^2 +y^2+4z^2 = 12#. How do you find the largest possible volume for the box?
1 Answer
Sep 14, 2016
Explanation:
The box volume is given by
so the problem is:
Find
Using Lagrange multipliers we have the equivalent problem
Find the stationary points of
and verify the solutions which give a maximum for
The stationary ponts are obtained by solving for
The solution is