Constructing an Open Box An open box with a square base to be made from a square piece of...

Constructing an Open Box An open box with a square base to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides. See the figure.

(a)  Express the volume V of the box as a function of the length x of the side of the square cut rom each corner.

(b)  What is the volume if a 3-inch square is cut out?

(c)  What is the volume if a 10-inch square is cut out?

(d)  Graph V = V(x).For what value of x is V largest?