My derivative is f'(x) = 6x/(x^2+3)^2
so the critical point should be: 6x = 0 and (x^2+3)^2 = 0
therefore x = 0
but I cannot solve for (x^2+3)^2 = 0
Yes, you are right. That will always be greater than 0. So you have just one test point at x=0. Make a number line and mark 0 on it. Test a number the left and right by plugging it into the derivative and see if the result is positive or negative. If you have a change from one sign to the other at x=0, then (0, f(0)) is your critical point.