Differential Equations: Population Growth: Logistic Equation: Example 2

In this video I prove that the growth rate in a population, assuming it uses the logistic model, is fastest at half the carrying capacity. I prove this using the first derivative test but apply it to the 1st and 2nd derivatives of the population function. In my last video I graphically showed that in fact the population appears to be growing fastest at about the half way mark, but in this video I prove it definitely. This is a very good video to understand how population sizes increase so make sure to watch this video!

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I don't always view models of population growth but when I do the fastest growth rate is usually at half the carrying capacity ;)