Significance of Inflection Points in Biological Application This problem appears in our calculus book. It asks to compute the maximum concentration of drug in the blood and the time when the maximum occurs as well as to find the number of inflection points and then it asks for the time at which the inflection points occur and finally the "significance" of the inflection points. The model given is 
$$C(t)=0.5t^2e^{-0.6t}$$
where $C(t)$ is the concentration. It was very easy to find that the maximum concentration of $\frac{50}{9}e^{-2}$ occurs at $t=10/3$ and that there are two inflection points, occurring at $t=\frac{10\pm 5\sqrt{2}}{3}$. But when the author asks for the "significance" of the inflection points I'm not sure what he means. An inflection point is a zero of the second derivative occurs. It is where the graph is "flat" (i.e. the curvature is zero) but in this case I believe the author wants the "biological" significance, and there I am stuck. Is it when the drug is being absorbed and excreted? Perhaps there is something about drug metabolism that I need to know and do not? Thank you in advance for any help!
When "the rate of variation of $C(t)$ is maximal" you would expect maximum effect of the drug at that time $t$.  For example: one has headache and takes the pain killer drug, at $t=23$ min, he will have maximum effect of the drug.

A better example: an antibiotic for infection. The guy should take tablets regularly every 8 hours and the maximum effect of the drug is at $t=4$ hours.  In real research, these times should be computed in trials to be able to say how often a tablet should be taken (dosage and many other things of the tablet are important as well).

Thanks Did for answer.
When "the rate of variation of $C(t)$ is maximal" you would expect maximum effect of the drug at that time $t$.  For example: one has headache and takes the pain killer drug, at $t=23$ min, he will have maximum effect of the drug.

A better example: an antibiotic for infection. The guy should take tablets regularly every 8 hours and the maximum effect of the drug is at $t=4$ hours.  In real research, these times should be computed in trials to be able to say how often a tablet should be taken (dosage and many other things of the tablet are important as well).

Thanks Did for answer.