Question

An open box is to be made by cutting squares of the same size
from the corners of a 12 cm by 12 cm square piece of cardboard
and then folding up the side. Find the size of a square to be cut
o so that the resulting box will enclose a maximum volume.
Find the maximum volume of the box.

Answer 1

if the squares have side length x, then the volume
v = 4x(x-6)^2
dv/dx = 12(x-2)(x-6)
max volume is when dv/dx=0, so we get v(2) = 128