Question
The strength of a human body's reaction $R$ to a dosage $D$ of a certain drug is given by$$R=D^{2}\left(\frac{k}{2}-\frac{D}{3}\right)$$where $k$ is a positive constant. Show that the maximum reaction is achieved if the dosage is $k$ units.
Step 1
This is given by $$ \frac{dR}{dD}=2D\left(\frac{k}{2}-\frac{D}{3}\right)+D^{2}\left(-\frac{1}{3}\right). $$ Simplifying this, we get $$ \frac{dR}{dD}=kD-D^{2}. $$ Show more…
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