Suppose that
$$f(x) = \frac{7e^x}{7e^x + 7}$$
(A) Find all critical values of $f$. If there are no critical values, enter the word "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, use inf for $\infty$, -inf 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:
