A firm's cost curve is C = F + 10q - bq2 + q3, where b > 0.
a. For what values of b are cost, average cost, and average variable cost positive? (From now on, assume that all these measures of cost are positive at every output level.)
b. What is the shape of the AC curve? At what output level is the AC minimized?
c. At what output levels does the MC curve cross the AC and the AVC curves?
d. Use calculus to show that the MC curve must cross the AVC at its minimum point?