Suppose that $$f(x) = 10 x e^{-0.4 x}.$$

(A) Find all critical values of $f$. If there are no critical values, enter "none" If there are more than one, enter them separated by commas.
Critical value(s) =

(B) Use interval notation to indicate where $f(x)$ is increasing.

Note: When using interval notation in WeBWorK, you use INF for $\infty$, -INF for $-\infty$, and 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 relative maxima of $f$. If there are no relative maxima, enter "none". If there are more than one, enter them separated by commas.

Relative maxima at $x$ =

(E) Find the $x$-coordinates of all relative minima of $f$. If there are no relative minima, enter "none". If there are more than one, enter them separated by commas.

Relative minima at $x$ =

(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 inflection points of $f$. If there are no inflection points, enter "none". If there are more than one, enter them separated by commas.
Inflection point(s) at $x$ =

Hint: