The given function is,
[tex]T=-0.023t^2+0.5014t+97.5[/tex]
The time t when the patient's temperature reache the maximum,
[tex]\begin{gathered} \frac{dT}{\differentialDt t}=0 \\ -0.046t+0.5014=0 \\ t=\frac{0.5014}{0.046} \\ t=10.9\text{ hr} \end{gathered}[/tex]
Thus, the patient's temperature is maximum at after 10.9 hours.
The patient's maximum temperature can be determined as,
[tex]\begin{gathered} T(10.9)=-0.023(10.9)^2+0.5014(10.9)+97.5 \\ =100.23 \end{gathered}[/tex]
Thus, the maximum temperature is 100.23 degree Farenheit.
