\(\displaystyle f(x)=\displaystyle\frac{x}{1+x^2}\)

I've calculated its second derivative (and the first ofcourse, I'll just post the second couse I have an exam tomorrow so I don't have much time).

\(\displaystyle f''(x)=\displaystyle\frac{-2x(3-x^2)}{(1+x^2)^3}\)

So, when I make f''(x)=0 I got \(\displaystyle {0,\sqrt[ ]{3}-\sqrt[ ]{3}}\) These three values. Now, I must analize which of them is an inflection point, and which is not. And for this I must "look" on a "ball" around the candidates. How may I do that?