Given the following short-run production function (x = variable input, Q = output):
Q = 3x2 - 0.1x3
(a) Determine the marginal product function (MPx) and the average product function (APx ).
(b) Find the value of x that maximizes Q.
(c) Find the value of x for which MPx is maximum.
(d) Find the value of x for which APx is maximum.
(e) Determine the boundaries of the three stages of production