Question

The concentration C(t), in milligrams per cubic centimetre, of a certain medicine in a patient's bloodstream is given by C(t)= (0.1t)/(t+3)^2 where t is number of hours after the medicine is taken. Determine the maximum and minimum concentrations between the first and sixth hours after the medicine is taken.

How did the book get answer max t=3 and min t=1

Answer 1

Find the derivative using the quotient rule
C'=(.1(t+3)^2-(2t+6)(.1t))/(t+3)^4
find where .1(t+3)^2 - (2t+6)(.1t) = 0
solving for t
t = 3
Evaluate C(1)
C(3) and C(6)
C(3) gives the maximum value, C(1) gives the minimum