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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
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avatar+86649 
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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 )

 

 

cool cool cool

CPhill  Feb 24, 2018

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