Suppose that $f(x) = x^3 - 3 x^2 + 1$.

(A) List all the critical values of $f(x)$. Note: If there are no critical values, enter 'NONE'.

(B) Use interval notation to indicate where $f(x)$ is increasing.
Note: Use 'INF' for $\infty$, '-INF' for $-\infty$, and use 'U' for the union symbol.
Increasing:

(C) Use interval notation to indicate where $f(x)$ is decreasing.
Decreasing:

(D) List the $x$ values of all local maxima of $f(x)$. If there are no local maxima, enter 'NONE'.
$x$ values of local maxima =

(E) List the $x$ values of all local minima of $f(x)$. If there are no local minima, enter 'NONE'.
$x$ values of local minima =

(F) Use interval notation to indicate where $f(x)$ is concave up.
Concave up:

(G) Use interval notation to indicate where $f(x)$ is concave down.
Concave down:

(H) List the $x$ values of all the inflection points of $f$. If there are no inflection points, enter 'NONE'.
$x$ values of inflection points =

(I) Use all of the preceding information to sketch a graph of $f$. When you're finished, enter a "1" in the box below.