If I had an equation $F(t)$ = $t$ $e^{\frac{-t}{10}}$ that modelled the concentration of a chemical with respect to time (where $t$ represented time in minutes).
If I wanted to find the time when the concentration of the drug decreased at the fastest rate, why would that be where the point of inflection is?
How would I find the time when the rate of increase was a maximum?
For reference:
I found $F'(t)$ = $e^{\frac{-t}{10}}$ ($\frac{-t}{10}$ +1)
And I found $F''(t)$ = $e^{\frac{-t}{10}}$ ($\frac{t}{100}$ - $\frac{1}{5}$)