Consider the following short-run production function (where L = variable input, Q = output): Q = 6L3

Question:

Consider the following short-run production function (where L = variable input,
Q = output):
Q = 6L3 − 0.4L3
a. Determine the marginal product function (MPL).
b. Determine the average product function (APL).
c. Find the value of L that maximizes Q.
d. Find the value of L at which the marginal product function takes on its maximum value.
e. Find the value of L at which the average product function takes on its maximum value.