An open box is to be made using one metre square of cardboard .find the maximum value of the box given that it has a square base
If x-cm cuts are made, the base is 100-2x cm, and the height is x cm.
The area is thus
(100-2x)^2 + 4x(100-2x) = 100^2
x = 2500/(100-2x) - 4(100-2x)
The volume is
v = x(100-2x)^2
= (2500/(100-2x) - 4(100-2x))(100-2x)^2
Now expand that, take dv/dx=0 and find x for maximum volume.
see the graph of v at
http://www.wolframalpha.com/input/?i=%282500%2F%28100-2x%29+-+4%28100-2x%29%29%28100-2x%29^2+for+35%3C%3Dx%3C%3D65