2/3
90%
(c) Now consider the particular parameter values \(C = 2\), \(\alpha = 0.3\) and \(\beta = 0.5\); that is,
\(c(t) = 10(e^{-0.3t} - e^{-0.5t})\),
where time \(t\) is measured in hours, and concentration \(c(t)\) is in \(\mu g/mL\).
\(\bullet\) What are the maximum and minimum concentrations of the antibiotic during the
first 18 hours after injection?
\(\bullet\) Use the second derivative test to show that that the internal extremum at some time
\(t_m\) with \(0 < t_m < 18\) is indeed a maximum.
\(\bullet\) Also find the time \(t_i\) at which the inflection point occurs.
(d) Sketch the graph of \(c(t)\) for \(t \in [0, 18]\). Indicate the maximum value, minimum value and
inflection point on your graph.
