# Thread: help with this derivative problem

1. ## help with this derivative problem

1. The problem statement, all variables and given/known data
-5.978(1+5.71e^-.054x)/1+5.71e^-.054x
logistical regression values from ti 83
a=5.71
b=.054
c=5.978

2. Relevant equations
general logistical regresion model g(x) c/1+ae^-bx
3. The attempt at a solution
So far I have applied the quotient rule to find the derivative of the general logistical model and come out to
(1+ae^-bx)-c(1+ae^-bx)/(1+ae^-bx)^2
I took derivate and factored a little and came to this
-c(1+ae^-bx)/1+ae^-bx
At this point I just factored in the logistical information from my ti 83 which is
a=5.71
b=.054
c= 5.978

I really need help factoring the numerator of this problem, and from there finding the 2nd derivative. I know at some point I must take natural log to both side of the equation to find the point of inflection. Please help me with this!

2. Originally Posted by goatrance
2. Relevant equations
general logistical regresion model g(x) c/1+ae^-bx
3. The attempt at a solution
So far I have applied the quotient rule to find the derivative of the general logistical model and come out to
(1+ae^-bx)-c(1+ae^-bx)/(1+ae^-bx)^2
I took derivate and factored a little and came to this
-c(1+ae^-bx)/1+ae^-bx
At this point I just factored in the logistical information from my ti 83 which is
a=5.71
b=.054
c= 5.978
This is confusing! What is your model? Is it
g(x) = c/(1 + ae^{-bx})?

If so then you have the first derivative wrong.
g'(x) = c/(1 + ae^{-bx})^2 * a*(-b)e^{-bx}

g'(x) = -abc*e^{-bx}/(1 + ae^{-bx})^2

-Dan

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