calculus
posted by george .
a box with no top is to be built by taking a 12''by16'' sheet of cardboard and cutting xinch squares our of each corner and folding up the sides. find the value of x that maximizes the volume of the box

If you cut out corner squares with length x , the height of the box is x and the base dimensions are (122x) * (16  2x)
Box volume V = x(122x)(162x)
(0 < x < 6)
V = 192x 56x^2 + 4x^3
Set the derivative dV/dx = 0 and solve for x