Chapter 4.3, Problem 59E

Drug Reaction The strength of a person’s reaction to a certain drug is given by

$R\left(Q\right)=Q{\left(C-\frac{Q}{3}\right)}^{\frac{1}{2}},$

Where $Q$ represents the quantity of the drug given to the patient and $C$ is a constant.

a. The derivative $R^{\text{'}}\left(Q\right)$ is called the sensitivity to the drug. Find $R^{\text{'}}\left(Q\right)$.

b. Find the sensitivity to the drug if $C=59$ and a patient is given 87 unit of the drug.

c. Is the patient’s sensitivity to the drug increasing or decreasing when $Q=87?$