Chapter 4.5, Problem 4QCE

An open box is to be made from a $20\text{-inch}$ by $32\text{-inch}$ piece of cardboard by cutting out $x\text{-inch}$ by $x\text{-inch}$ squares from the four corners and bending up the sides. The largest possible volume of the box is obtained by maximizing $V\left(x\right)=\text{\_\_\_\_\_\_\_\_}$ for $x$ in the interval $\text{\_\_\_\_\_\_\_\_\_}$ .