Another word problem (Maximum Volume of folded-up box)

[Linty Fresh]

A candy box is to be made out of a piece of cardboard that measures 8 x 12 inches. Squares of equal size will be cut out of each corner, and then the ends and sides ill be folded up to form a rectangular box. What size square should be cut from each corner to obtain a maximum volume?

OK, here's what I've got:

Let x=one side of the square to be cut out of the corner
length of box=12-2x
width of box=8-2x
height of box=x

Volume=lwh
V(x)=(8-2x)(12-2x)(x)
=(96-16x-24x+4x^2)x
=(96-40x+4x^2)(x)
=96x-40x^2+4x^3

V'(x)=96-80x+12x^2

Set V'(x) to 0 to get the max volume, and use the quadratic formula to solve, but I'm not getting the right value for "x" according to the answer key. Have I set the problem up incorrectly? Thanks so much.

 

[galactus]

You have the correct equation to solve.

The 2 solutions to the quadratic are:

1.57 and 5.1

Of course, the 1.57 is the sensible one.

Is that what you got?.

 

[Linty Fresh]

OK, that's what I'm getting now. I must have made a careless error in the quadratic formula somewhere.

Many thanks!