What is the point of maximum growth rate for the logistic function f(x)? Round to the nearest hundredth.

(0.42, 3)

(0.85, 12)

(0.85, 24)

(0, 4)

jbouyer
Feb 24, 2018

#1**+2 **

Write this as

y = 24 [1 + 3e^(-1.3x)]^(-1)

The derivative of this function is

y ' = -24[ 1 + 3e^(-1.3x)]^(-2) ( -3.9e^(-1.3x))

Looking at the graph of the derivative here :

https://www.desmos.com/calculator/sunmexdhiz

We see that the max growth rate occurs at about x = .845

The graph of the function here :

https://www.desmos.com/calculator/pkls30n5mn

Shows that the y value associated with this x value = 12

So....the max growth rate occurs at ≈ (.85, 12 )

CPhill
Feb 24, 2018