A square sheet of cardboard with a side 16 inches is used to make an open box by cutting squares of equal size from the four corners and folding up the sides. What size squares should be cut from the corners to obtain a box with largest possible volume?

Answer 1

v = x(16-2x)^2 = 2x(8-x)^2
dv/dx = 4(3x-8)(x-8)
x=8 is obviously a minimum (v=0), so
max volume is at x = 8/3