It is often difficult to evaluate the quality of products that undergo a ripening or maturation process. Researchers have successfully used ultrasonic velocity to determine the maturation time of Mahon cheese. The age can be determined by

M(v) = 0.0312443v² - 101.39v + 82,264, v ≥ 1620,

where M(v) is the estimated age of the cheese (in days) for a velocity v (m per second).

(a) If Mahon cheese ripens in 150 days, determine the velocity of the ultrasound that one would expect to measure. Set M(v)  = 150 and solve for v.)
(b) Determine the derivative of this function when v = 1700 m per second and interpret.