A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 66 inches (see figure).

Question

Find the dimensions of the package of maximum volume that can be sent. (Assume the cross section is square.)

Answer 1

s represents the side of the cross section (a square)

66 - 4s represents the length

V = (66 - 4s)s²

V = -4s³ + 66s²

V' = -12(s² - 11s)

At what value of s is V' maximum?