Question

Algebra 2: To create an open-top box out of a sheet of cardboard that is 4 inches long and 2 inches wide, you make a square flap of side length x inches in each corner by cutting along one of the flap's sides and folding along the other. (In the diagram, a solid line segment in the interior of the rectangle indicates a cut, while a dashed line segment indicates a fold.) Once you fold up the four sides of the box, you glue each flap to the side it overlaps. To the nearest tenth, find the value of x that maximizes the volume of the box.