f(x)= 2x/(x^2+1)

Vertical: none
Horizontal: none
Minimum: x=-1
Maximum: x=1
Inflection Points: it seems like there are one or two, but i don't know how to factor f''(x)= 4x^3 + x^2 - 12x + 1 :/

Can someone help me with this? I have already solved it. Thank you.