# A certain population is known to be growing at a rate given by the logistic equation dx/dt=x(b-ax) Show that the minimum rate of growth will occur when occur when the population is equal to half the equilibrium size,that is,when the population is b/2a?

##### 1 Answer

Jul 1, 2018

To optimise growth rate, take its derivative and set to zero:

The next derivative confirms the nature of the critical point: