A beekeeper has found a logistic model for the population growth of their beehive. If $f(x)$ is the model, find the point at which the population is having its most rapid growth $($i$.$e the inflection point$).$ Provide the $x-$value with units as your answer.

$f(x)=\frac{30}{3+6e^{-\mathrm{.}11x}}$ thousand bees for $x$ days $of$ ownership