Question 8.2.1: Measured in milligrams per litre, the concentration of a dru......

Differentiating with respect to t yields

For t ≥ 0, the term 2 − t alone determines the sign of the fraction, because the other terms are positive: if t ≤ 2, then c^{\prime}(t) ≥ 0; whereas if t ≥ 2, then c^{\prime}(t) ≤ 0.We conclude that t = 2 maximizes c(t). Thus, the concentration of the drug is highest two hours after injection. Because c(2) = 0.25, the maximum concentration is 0.25 mg.