Logistic growth and phase lines practice question 5

The growth rate $\dfrac{dP}{dt}$ is an ordinary function of $P$. Where is that function largest, and what is its value there?

The growth rate is a function of the population: $G(P) = 0.5P - 0.0001P^{2}$. To find where it is largest, set $G'(P) = 0$, not $G(P) = 0$.

$G'(P) = 0.5 - 0.0002P$. Solve for $P$, then substitute that population back into $G$.