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Math Help - Finding Critical Points of Functions

  1. #1
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    Finding Critical Points of Functions

    Hello, and thanks in advance for the help.

    I need to find the critical numbers of the function listed below. I understand that critical numbers mean one of two things, that the derivative at the point where x is critical is 0, or that the derivative does not exist.

    It may simply be a simplification issue, but I'm having trouble solving for this derivative in a way that ti s manageable.

    h(p) = (p-1)/(p^2+4)

    Thanks again for the help!
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  2. #2
    ux0
    ux0 is offline
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    h(p)=\frac{p-1}{p^2+4}

    Just use the quotient rule..

    h'(p)=\frac{(p^2+4)-(p-1)2p}{(p^2+4)^2}


    h'(p)=\frac{-p^2+2p+4}{(p^2+4)^2}

    use the quadratic formula and get the roots of the numerator and you will have your maximum or minimum values..Also we know there is no value of p that would set the numerator zero in the real numbers... so there is no asymptotes.
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