One hour after x milligrams of a particular drug are given to a person, the change in body temperature T(x), in degrees Celsius, is given approximately by: T(x) = $\frac { 5 x ^ { 2 } } { 9 }$ $\left. 1 - \frac { x } { 9 } \right)$ - $\frac { 160 } { 9 }$ , 0 ≤ x ≤ 6. Find the sensitivity, T'(x), of the body to a dosage of three milligrams.
A) $\frac { 5 } { 3 }$ degrees per milligram
B) - $\frac { 10 } { 9 }$ degrees per milligram
C) - $\frac { 5 } { 3 }$ degrees per milligram
D) - $\frac { 10 } { 27 }$ degree per milligram

Question

Quizplus · Accepted Answer

To find the sensitivity, T'(x), we need to differentiate T(x) with respect to x. The derivative of T(x) = $\frac { 5 x ^ { 2 } } { 9 }$ $\left( 1 - \frac { x } { 9 } \right)$ - $\frac { 160 } { 9 }$ is T'(x) = $\frac { 10 x } { 9 }$ - $\frac { 5 x ^ { 2 } } { 81 }$. Plugging in x = 3, we get T'(3) = $\frac { 10 \cdot 3 } { 9 }$ - $\frac { 5 \cdot 9 } { 81 }$ = $\frac { 30 } { 9 }$ - $\frac { 45 } { 81 }$ = $\frac { 10 } { 3 }$ - $\frac { 5 } { 9 }$ = $\frac { 30 - 5 } { 9 }$ = $\frac { 25 } { 9 }$, which simplifies to $\frac { 5 } { 3 }$ degrees per milligram.

One Hour After X Milligrams of a Particular Drug Are 5x29\frac { 5 x ^ { 2 } } { 9 }95x2​

One Hour After X Milligrams of a Particular Drug Are $\frac { 5 x ^ { 2 } } { 9 }$