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