Chapter 8, Problem 12P

To determine

(a)

The expression for the volume $V$ of a given rectangular box (open top) in terms of $x$ using polynomials.

To determine

(b)

To plot:

The volume $V$ in terms of $x$.

To determine

(c)

The value of $x$ if the volume of the box is $1000{\text{in}}^{\text{3}}$.

To determine

(d)

The value of $x$ that corresponds to the box with the largest possible volume, and determine that volume.