1. A cylindrical package to be sent by mail can have a maximum combined length and girth (perimeter of a cross section) of 147 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
2. Consider the following function.
f(x) = 2x3 + 6x2 - 90x
(a) Find the critical numbers of f.
(b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)