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.

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.

whpalmer4 · Answer

$$C(t) = \frac{0.016t}{(t+2)^2}$$
Differentiate that with respect to t, then set the result = 0 and solve for t.  That will be the time of the maximum concentration.  Use that value of t to find the concentration at that time.