Suppose that $$f(x) = \frac{4 e^x}{4 e^x + 5 }.$$

(A) Find all critical values of $f$. If there are no critical values, enter -1000. 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 I for $\infty$, -I for $-\infty$, and U for the union symbol. If there are no values that satisfy the required condition, then enter "{}" without the quotation marks.

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 -1000. 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 -1000. 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:

(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 -1000. If there are more than one, enter them separated by commas.
Inflection point(s) at $x$ =

(I) 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: