Critical points occur where $f^{\prime }(x)=0$ (or where the derivative does not exist). Use the second derivative test: if $f^{\prime \prime }(x_0)>0$ then $x_0$ is a local minimum; if $f^{\prime \prime }(x_0)<0$ then $x_0$ is a local maximum.

Let $f(x)=x^3-6x^2+9x+2$.

Find:

1. All critical points of $f$
2. Whether each is a local maximum or local minimum