A box is to be made out of a 6 cm by 18 cm piece of cardboard. Squares of side length $x$ cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) Express the volume $V$ of the box as a function of $x$.

$V =$ $\textrm{cm}^3$

(b) Give the domain of $V$ in interval notation. (Use the fact that length and volume must be positive.)

(c) Find the length $L$, width $W$, and height $H$ of the resulting box that maximizes the volume. (Assume that $W \leq L$).

$L$ = cm

$W$ = cm

$H$ = cm

(d) The maximum volume of the box is $\textrm{cm}^3$.