Logistic Growth Many populations grow according to the logistic equation (dx)/(dt)=rx(N-x)

Question: Logistic Growth Many populations grow according to the logistic equation

\[\frac{dx}{dt}=rx\left( N-x \right)\]

where r is a constant involving the rate of growth and N is the carrying capacity of the environment, beyond which the population decreases. Show that the graph of x has an inflection point where x = N/2.