Suppose that $$f(x) = \frac{3 x}{x^2 - 25}.$$

(A) Find all critical values of $f$. (A critical value is the value of $f$ at a critical point.) If there are no critical values, enter DNE. (DNE stands for "Do Not Exist"). If there are more than one, enter them separated by commas.

Critical value(s) =

(B) Use interval notation (not things like DNE) to indicate where $f(x)$ is increasing. How to enter intervals.

Increasing on

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

Decreasing on

(D) Find the $x$-coordinates of all local maxima of $f$. If there are no local maxima, enter DNE. If there are more than one, enter them separated by commas.

Local maxima at  $x$ =

(E) Find the $x$-coordinates of all local minima of $f$. If there are no local minima, enter DNE. If there are more than one, enter them separated by commas.

Local minima at  $x$ =

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

Concave up on

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

Concave down on

(H) Find all inflection points of $f$. If there are no inflection points, enter DNE. If there are more than one, enter them separated by commas.

Inflection point(s) at  $x$ =

(I) Find all horizontal asymptotes of $f$. If there are no horizontal asymptotes, enter DNE. If there are more than one, enter them separated by commas.

Horizontal asymptote(s):  $y$ =

(J) Find all vertical asymptotes of $f$. If there are no vertical asymptotes, enter -1000. If there are more than one, enter them separated by commas.

Vertical asymptote(s):  $x$ =

(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: