We want to find where the second derivative changes sign, so first we need to find the second derivative. The first derivative is *f *'(*x*) = 3*x*^{2}
and the second derivative is *f *"(*x*) = 6*x*.
The second derivative is never undefined, and the only root of the second derivative is *x* = 0. The sign of *f *" does change there, since *f*"(*x*) is negative for *x* < 0 and positive for *x* > 0. Therefore *x* = 0 is an inflection point. Looking at the graph of *f* (*x*), this makes sense: |