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Math Help - Curve Sketching

  1. #1
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    Curve Sketching

    I'm having trouble finding the point of inflection of the graph

    f(x)=(8e^x)/(e^(2x)+4)

    so I cannot find the points of inflection even though I know the procedure:

    f''(x)=(8e^x)/(e^(2x)+4)

    f''(x)= 0 and f''(x) = undefined both do not exist...soo there is no point of inflection right? no.. there has to be BECAUSE, when i graph the function, concavity is changing.
    from (-infinity, ln2) we have concave up and from (infinity,ln2) concave down. now... how do i find the point of inflection if i know that concavity is changing, but the second derivative does not allow me to find the point?

    other info:
    max point (ln2,2)
    HA=y=0
    yint=1.909
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  2. #2
    MHF Contributor red_dog's Avatar
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    f''(x)=\frac{8e^x(e^{4x}-24e^{2x}+16)}{(e^{2x}+4)^3}

    f''(x)=0\Rightarrow e^{4x}-24e^{2x}+16=0

    Put e^{2x}=t and solve the quadratic.
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  3. #3
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    i end up getting t= 23 and t=0.7

    when i graph the function, t=0.7 does look like a PI but t=23 seems way off.. what did you get?
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  4. #4
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    can anyone verify this???
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