An open-top box is to be constructed from a $6 \ \mbox{in}$ by $14 \ \mbox{in}$ rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let $x$ denote the length of the side of each cut-out square. Assume negligible thickness.

(a) Find a formula for the volume, $V$, of the box as a function of $x$. $\ \ V(x) =$

(b) For what values of $x$ does the formula from part (a) make sense in the context of the problem?
help (inequalities)

(c) On a separate piece of paper, sketch a graph of the volume function.

(d) What, approximately, is the maximum volume of the box?
(include units: help (units))