Answer
Maximum concentration: $4.5$ mg/L.
Time to reach maximum concentration: $150$ seconds.
Work Step by Step
$C(t)=-0.0002t^2+0.06t$
Although we know that $0\leq t\leq 240$, this does not provide us any information about maximum concentration, which is $C(t)$, not $t$. Therefore, we need to use our usual formula.
Maximum concentration occurs when: $x=\frac{-0.06}{-0.0004}=150$
Because $0\leq 150\leq240$, we can directly use this $x$ value to find the maximum concentration.
$C(150)=-0.0002*150^2+0.06*150=-0.0002*22500+9=-4.5+9=4.5$
In conclusion, we reach the maximum concentration of $4.5$ mg/L after $150$ minutes of taking the drug.
