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One hour after a dose of $x$ milligrams of a particular drug is administered to a person, the change in body temperature $T(x)$, in degrees Fahrenheit, is given app...

Question

One hour after a dose of $x$ milligrams of a particular drug is administered to a person, the change in body temperature $T(x)$, in degrees Fahrenheit, is given approximately by $$ T(x)=x^{2}\left(1-\frac{x}{9}\right) \quad 0 \leq x \leq 7 $$ The rate $T^{\prime}(x)$ at which $T$ changes with respect to the size of the dosage $x$ is called the sensitivity of the body to the dosage. (A) Use the product rule to find $T^{\prime}(x)$. (B) Find $T^{\prime}(1), T^{\prime}(3),$ and $T^{\prime}(6)$.

One hour after a dose of $x$ milligrams of a particular drug is administered to a person, the change in body temperature $T(x)$, in degrees Fahrenheit, is given approximately by $$ T(x)=x^{2}\left(1-\frac{x}{9}\right) \quad 0 \leq x \leq 7 $$ The rate $T^{\prime}(x)$ at which $T$ changes with respect to the size of the dosage $x$ is called the sensitivity of the body to the dosage. (A) Use the product rule to find $T^{\prime}(x)$. (B) Find $T^{\prime}(1), T^{\prime}(3),$ and $T^{\prime}(6)$.



Answers

Drug Concentration The concentration of a certain drug in the bloodstream $t$ hours after being administered is approximately
$$C(t)=\frac{5 t}{9+t^{2}}$$
Use the differential to approximate the changes in concentration for the following changes in $t$.
$\begin{array}{ll}{\text { (a) } 1 \text { to } 1.5} & {\text { (b) } 2 \text { to } 2.25}\end{array}$


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