Construct your own example of a function

Question

Problem

1. Construct your own example of a function that has a turning point. Check the second-order conditions to confirm whether this turning point is a maximum or a minimum.

2. A firm attempting to expand output in the short-run faces the total product of labour schedule TPL = 24L² - L³. At what levels of L will (a) TP_L, (b) MP_L, and (c) AP_L be at their maximum levels?

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.