Chapter 4.1, Problem 98E

Medicine. The concentration C(t), in milligrams per cubic centimeter, of a particular drug in a patient’s bloodstream is given by

     $\begin{array}{ll}C(t)=\frac{0.3t}{t^2+6t=9}\hfill & 0<t<12\hfill \end{array}$

where t is the number of hours after the drug is taken orally. Find the critical numbers of C(t), the intervals on which the drug concentration is increasing, the intervals on which the drug concentration is decreasing, and the local extrema. Do not graph.