The demand function for a certain product is given by: P(x) = 100 0.02x 2 + 1 where 0 x 20 and x (measured in units of a thousand) is the quantity demanded per week and P(x) is the unit price in dollars. (a) Find P 0 (x). (b) Find P 0 (10),P 0 (15), and P 0 (20) and interpret your results. (c) Derive the revenue function (Hint: revenue is determined by price times quantity). (d) Derive the marginal revenue function