# Math Help - concavity and inflection points

1. ## concavity and inflection points

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

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

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

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.

2. Originally Posted by hazecraze

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

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

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

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.