A minimum/maximum problem using the point of inflection

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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).

  1. 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?

  2. 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 $F''(t)$ = $e^{\frac{-t}{10}}$ ($\frac{t}{100}$ - $\frac{1}{5}$)