Cut equal squares from the four corners of a square sheet of paper and fold up the sides to make an open-top box. Adjust the cut size x and find the point where the volume is largest.
The volume of the box is V(x) = x(L-2x)². If x is too small, the box is too shallow; if x is too large, there is barely any base left. The volume is maximized at the point where the derivative V'(x)=0.