Question

The concentration of a drug in a patient's bloodstream t hours after it is taken after it is taken is given by
C(t) = 0.016t/(t+2)^2 mg/cm^3
Find the maximum concentration of the drug and the time at which it occurs.

Answer 1

The maximum concentration of the drug occurs when the derivative of C(t) is equal to 0.

C'(t) = 0.016(2t+2)/(t+2)^3

0 = 0.016(2t+2)/(t+2)^3

2t+2 = 0

t = -1

The maximum concentration of the drug occurs at t = -1 and is 0.016 mg/cm^3.