There has been an explosion of use of antibiotic for both medical and veterinary (especially in meat and poultry industry) purpose. The following cubic equation is an estimate of billion dozes of antibiotic used each year over 20-year time periods (t= 1 for year 1995),

A(t) = 0.192 t3 -2.305t2 +10.95t+12.06

a) Calculate A(10) and A'(10). What is the interpretation of A'(10)?

b) Show that the marginal function intersect the average function at its minimum point