This problem is from my brother's calculus class, so it is slightly over my head (I'm in pre-calc), but I am curious how to go about solving this problem.
Basically there is a rectangle with sides of $15$ units and $9$ units in length, and four squares with sides that have a length of $x$ are cut out of each corner.
If you fold up each of the sides so that it makes a 3-dimensional shape, how would you figure out the maximum volume of the shape?
Here's what I have so far:
$V = (15-2x)(9-2x)x$
$V = 4x^3 - 48x^2 + 135x$
That's about as far as I've gotten. Can anybody help?