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?
(d) What, approximately, is the maximum volume of the box? Give answer to at least 4 decimal places.
