Question 83177
If you can imagine the cardboard 6 feet by 8 feet, and you're cutting squares of side x from each corner.
The length of the box would be 8-2x, and the width would be 6-2x, and the height is x.
So the volume is {{{V=x(8-2x)(6-2x)}}}
The relevant range of values of x are from 0 to 3, since you can't have the cut-out squares having a larger side than half the width of the original rectangular cardboard..
The graph looks like this:
{{{ graph( 300, 200, -1, 3, -2, 30,x*(8-2x)*(6-2x)) }}} 
And the value of x which will give the maximum volume is approximately 1.13