The open-top box is to be made from the 4 in by 14 in rectangular sheet of tin by cutting out squares of equal size at every corner, then folding up resulting flaps. Let x signify length of side of each cut-out square. Suppose negligible thickness.
(a) Determine the formula for volume, V, of box as the function of x. V(x)=
(b) For what values of x formula from part (a) makes sense in context of problem?
(c) On the separate piece of paper, draw the graph of volume function.
(d) What, approximately, is maximum volume of box?