Step-by-step explanation:
Given that,
The temperature, T, in degrees Fahrenheit, of the patient t hours after the illness begins is given by:
[tex]T(t)=-0.02t^2 +0.4968 t+98[/tex] ...(1)
(a) We need to find when does the patient's temperature reach its maximum value.
For maximum value.
Put dT(t)/dt = 0
[tex]\dfrac{d(T(t)}{dt}=\dfrac{d}{dt}(-0.02t^2 +0.4968t +98)\\\\=-0.04t+0.4968\\\\-0.04t+0.4968=0\\\\t=12.42\ h[/tex]
(b) Put t = 12.42 in equation (1) :
[tex]T(12.42)=-0.02(12.42)^2 +0.4968 (12.42)+98\\\\=101.08^{\circ} F[/tex]
Hence, this is the required solution.
