# 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