The revenue (in thousands of dollars) from producing x units of an item is
R(x) = 10x - 0.002x².
(a) Find the average rate of change of revenue when production is increased from 1000 to 1001 units.
(b) Find and interpret the instantaneous rate of change of revenue with respect to the number of items produced when 1000 units are produced. (This number is called the marginal revenue at x = 1000.)
(c) Find the additional revenue if production is increased from 1000 to 1001 units.
(d) Compare your answers for parts (a) and (c). What do you find? How do these answers compare with your answer to part (b)?