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Math Help - help with this derivative problem

  1. #1
    goatrance
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    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!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by goatrance View Post
    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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