Note that
and
AVC = 10 - bq + q^2,
dAVC/dq = 2q - b.
Use calculus to show that the marginal cost curve, MC, must cross the average variable cost curve, AVC, at its minimum point.
A. AVC is at its minimum point when ($-F/q^2$) - b + 2q = 0, at which output level MC, which is 10 - 2bq + 3q^2, equals AVC.
B. AVC is at its minimum point when q = b/2, at which output level MC, which is 10 - 2bq + 3q^2, equals AVC.
C. AVC is at its minimum point when b < (10 + q^2)/q, at which output level MC, which is 10 - 2bq + 3q^2, equals AVC.
D. AVC is at its minimum point when q = b/2, at which output level MC, which is (F/q) + 10 - bq + q^2, equals AVC.
E. AVC is at its minimum point when q = b/2, at which output level MC, which is 10 - 2bq + 3q^2 and AVC both equal zero.
