"Find the volume of the largest open box.."
Here's the problem:
"Find the volume of the largest open box that can be made from a piece of cardboard 24 inches square by cutting equal squares from the corners and turning up the sides."
I have no provided diagram, the answer is 1024 cubic inches.
Here's what I've done:
y = z, y*z = 24.
y=z=square root of 24 - 2x, substitute into the equation for volume, differentiate, set v'(x) = 0, solve, figure out which one doesn't break my domain, substitute into the original equation...and it doesn't work.