# concavity and inflection points

• Oct 30th 2009, 12:23 PM
hazecraze
concavity and inflection points
http://www.webassign.net/cgi-bin/sym...28x%5E2%2B3%29
http://img215.imageshack.us/img215/3230/37220629.jpg
----------------------
$\displaystyle f'(x)=\frac{6x}{(x^2+3)^2}$

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

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

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.
• Oct 30th 2009, 01:47 PM
skeeter
Quote:

Originally Posted by hazecraze
http://www.webassign.net/cgi-bin/sym...28x%5E2%2B3%29

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

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

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

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 ...

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

fix it.