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, \(V\text{,}\) of the box as a function of \(x\text{.}\) \(\ \ V(x) =\)

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

(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: )