Suppose that $$f(x) = 3 x^5 - 5 x^4.$$
(A) Find all critical numbers of $f$. If there are no critical values, enter 'NONE'.
critical numbers =

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

(E) Find the $x$-coordinates of all local minima of $f$. 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) Find all $x$ values of the inflection points of $f$. If there are no inflection points, enter 'NONE'.
$x$ values of inflection points =

(I) Find all horizontal asymptotes of $f$, If there are no horizontal asymptotes, enter 'NONE'.
Horizontal asymptotes $y =$=

(J) Find all vertical asymptotes of $f$. If there are no vertical asymptotes, enter 'NONE'.
Vertical asymptotes $x=$

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