Answer
Maximum steady state concentration is $775.24 mcg/mL$.
Minimum steady state concentration is approximately $185 mcg/mL$.
Work Step by Step
The steady-state concentration function is given by,
$C_{ss}(t)=1.99De^{-0.14t}-1.62De^{-2.08t} mcg/mL$
$D$ is the size of the dose in milligrams administered every $12 hrs$.
When $D=500 mg$, $C_{ss}(t)=995e^{-0.14t}-810e^{-2.08t} mcg/mL$
At critical points, $C'_{ss}(t)=0$.
$C'_{ss}(t)=-139.3e^{-0.14t}+1684.8e^{-2.08t}$
$C'_{ss}(t)=0 \implies t=1.285 hrs$.
$C_{ss}(1.285)=775.24 mcg/mL$
$C_{ss}(1)=763.817mcg/mL$
Therefore we can conclude that at $t=1,285 hrs$ the steady-state function is maximum.
At $t=0 $ and $t=12$, $C_{ss}(t)\approx185 mcg/mL$ which is the minimum steady- state concentration.
