I am suppose to find the volume if 1200 cm^2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
I think what I need to do is set up the formulas to be
$4(lw) + w^2 = 1200$ for area
$lwh = v$ for volume
I know that if the base is a square than the rectangle will have the same dimensions and the only different variable would be the height so I can solve for length like so
$l=\frac{1200-w^2}{4w}$
Now that I have that I can put it in my formula
$lwh = v$ for volume
which I can rewrite as
$l^2 * h = v$
I then take the derivative of this and I get some ridiculous answer that is wrong.
$\frac{1200w^2 - w^4}{4w}$
the derivative
$300 \frac{-3w^2}{4}$
Which gives me $+-20$ which is an incorrect answer.