After taking a painkiller pill, that amount of a drug present in the bloodstream

Question

After taking a painkiller pill, that amount of a drug present in the bloodstream increases until It reaches a maximum quantity (this occurs once the entire pill has been absorbed). Then, as the drug is metabolized and broken down in the kidneys, the amount of drug present in the bloodstream decreases until it reaches an immeasurable level. the function D models the number of milligrams of drug present in the bloodstream t hours after swallowing the painkiller pill. d(t) = 2.4t/t^2 +5.29 How many hours does it take for the drug concentration to reach a maximum? The answer should be a fairly nice value that will not require any rounding. Answer It will take t = hours to reach a maximum.

Explanation / Answer

Using derivatives

first derivative=126960-24000t^2/(100t^2+529)^2

equate the above to 0

t (max)=23/10

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