Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable. (If an answer does not exist, enter DNE.)

g(x)=x^(3)-9x

f' = 3x^2-9

so, any extrema will be at x = sqrt(3) or -sqrt(3)
f'' = 6x, so it is not zero there.
So, both values are critical values.