In Figure, the total benefit and total cost curves are represented by the following mathematical functions: 

TB = TB (A) = 8A – 0.004 A²

and 

TC = TC (A) = A + 0.006 A²

a. Find the marginal benefit function. Verify that points c, b, and d in Figure lie on the marginal benefit curve. 

b. Find the marginal cost function. Verify that points c’, b, and d’ in Figure lie on the marginal cost curve. 

c. Derive the net benefit function. Verify the slopes of net benefit at points M, c”, and d” in Figure. 

d. Find the optimal level of activity and the maximum value of net benefit. Does your answer match Figure?