I would like help understanding how to answer this question, it was seen in class and I'm confused how my teacher got the answers, thank you in advance!

Assume that the production function for the removal of atmospheric carbon is as follows:

Q = MN - 0.8M² - 0.2N², where M= human-made capital and N= natural capital.

a) Re-write the production function given a level of human-made capital of 10 units. Find its maximum point. Then, find the average natural capital productivity (AP_N). Find where the AP_N reaches maximum.

b) Find the marginal productivity of natural capital (MP_N). At what value of N is MP_N zero?

c) Graph the production function and label of its maximum point of output. On a separate graph, draw the MP_N and the AP_N functions as functions of natural capital. Label point (Value of N) for which AP_N is at its maximum.