Here's another question Ive come across during revision

So

Volume is

$\displaystyle w*d*h = 32000$

$\displaystyle w^2*h = 32000$

$\displaystyle h = \frac{32000}{w^2}$

Total area is base of box + 4 sides -

$\displaystyle w^2 + 4wh$

$\displaystyle w^2 + \frac{128000}{w}$

And then I got the derivative of $\displaystyle f(x) = w^2 + \frac{128000}{w}$

And where this derivative = 0, there was a local minimum. This was where w = 40, so that makes d = 40 and h = 20 for the dimensions of the box that will use the minimum amount of material.

I take it this is all correct?

If it is, what I'm wondering is how I would be able to find the dimensions that would use themaximumamount of material? I only got one critical point when differentiating and that turned out to be a local minmum so how is it possible to find the maximum amount of material used?