Maximizing Volume: Rectangular Box Inscribed in an Ellipsoid

[Dissonance in E]

Homework Statement

Find the volume of the largest rectangular box with faces parallel to the coordinate planes that can be inscribed inside the ellipsoid :

(x^2/a^2)+(y^2/b^2)+(z^2/c^2) = 1

Homework Equations

Volume of a rectangular box = x * y * z
critical point formula.

The Attempt at a Solution

The volume of a box is maximised when x = y = z ?

 

[Coto]

Not quite. Try rewriting x in terms of y and z and plugging this into your volume formula. This must hold since x is determined by y and z (i.e. the vertices of the rectangular box will lie on the ellipsoid.)

Now, how do you find the maximum of a function of one variable? How do you find the maximum of a function of two variables?