Graphing calculator SCORE:
100 points
1. A machine produces open boxes using rectangular sheets of metal measuring
24 x 18 inches. The machine cuts equal-sized squares from each corner.
Then it shapes the metal into an open box by turning up the sides. (10 points)
a.
b.
c.
d.
a. Express the volume of the box, V, in cubic inches, as a function of the length of the side of
the square cut from each corner, x, in inches.
b. Find the domain of V.
c. Find the value of x, that maximizes the box's volume. (Round to the nearest thousandth)