Identify the open intervals on which the graph of f(x)=3/(x^2+12) is concave up and/or concave down.
Please give in interval form.
By now you should know all about the 2nd derivative:
f is concave up where f'' > 0
Find f'', find its roots, and note where it's positive.
Just to help out,
f''(x) = 18(x^2 - 4)/(x^2 + 12)^3
If that doesn't help, you're in big trouble!