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Math Help - concavity and inflection points

  1. #1
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    concavity and inflection points



    ----------------------
    f'(x)=\frac{6x}{(x^2+3)^2}

    f"(x)=\frac{6(x^2+3)-24x^2(x^2+3)}{(x^2+3)^2}

    f"(x)=\frac{6-24x^2}{(x^2+3)}

    x= + or - 1/2 and + or - sqrt(3). I was going to do the sign chart/number line method where you plug in points, by my intervals are different.
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  2. #2
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    Quote Originally Posted by hazecraze View Post


    ----------------------
    f'(x)=\frac{6x}{(x^2+3)^2}

    f"(x)=\frac{6(x^2+3)-24x^2(x^2+3)}{(x^2+3)^2}

    f"(x)=\frac{6-24x^2}{(x^2+3)}

    x= + or - 1/2 and + or - sqrt(3). I was going to do the sign chart/number line method where you plug in points, by my intervals are different.
    your 2nd derivative is incorrect ...

    f''(x) = \frac{6(x^2+3)^2 - 24x^2(x^2+3)}{(x^2+3)^4}

    fix it.
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