An open-top box is to be constructed from a 8 in by 14 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? (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: (units))