I have to sketch the graph of this function f(x) = (2x)/(x^2 - 4)

As First derivative I obtained f'(x)= - 2(x^2 + 4)/[(x^2-4)^2] and NO critical numbers are found;

I evaluated the function and it gives me that f(x) is decreasing from (-INF, -2)U(-2,2)U(2, INF)

I didn't find any local minima or local maxima for that function

for the second derivative, it gave me f"(x)=[4x(x^2 + 12)]/[x^2-4]^3

I obtained (0) as points of inflection, and...

the graph is CU on (-2, 0)U(2, INF)

and CD on (-INF, -2)U(0, 2)

horizontal asymtote is y=0

vertical asymtotes are x = -2 or x=2

I Checked something and my graph is correct in this way

Thanks everybody