The owners of an oil reserve begin extracting oil at time t = 0. Based on estimates of the reserves, suppose the projected extraction rate is given by Q'(t) = 3t² (40 - t)², where 0 ≤ t ≤ 40, Q is measured in millions of barrels, and t is measured in years. 

a. When does the peak extraction rate occur?

b. How much oil is extracted in the first 10, 20, and 30 years?

c. What is the total amount of oil extracted in 40 years?

d. Is one-fourth of the total oil extracted in the first one-fourth of the extraction period? Explain.