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!