What function should be used to maximize the volume of an open box whose surface area is equal to 20 where the box has a square bottom?

Surface area = x^2 + 4 x h , where x is the base side and h is the height
SA = x^2 + 4 x h = 20
4xh = 20-x^2
h = (20-x^2) / (4x)

Volume = x^2 h
Volume = x^2 (20-x^2) / (4x)
Volume = (1/4) x (20-x^2)
Volume = (1/4) (20x-x^3) ------> this is the function used to maximize the volume

dV/dx = (1/4) (20-3x^2) = 0
3x^2 = 20
x^2 = 20/3
x = sqrt(20/3) = 2,582
h = (20- x^2) /(4x) = (20 - (2.582)^2 ) / ( 4*2.582) = 1.291

d^2V/dx^2 = (-3/4) (2x) = (-3/2) x < 0 when x= 2.582 so V has been maximized.

Maximum volume = x^2 h = (2.582)^2 (1.291) = 8.6067