Consider the function $$f(x)=\frac{e^x}{4 + e^x}$$
Then $f'(x)$ =
The following questions ask for endpoints of intervals of increase or decrease for the function $f(x)$.
Write INF for $\infty$, MINF for $-\infty$, and NA (ie. not applicable) if there are no intervals of that type.

The interval of increase for $f(x)$ is from
to
The interval of decrease for $f(x)$ is from
to
$f(x)$ has a local minimum at . (Put NA if none.)
$f(x)$ has a local maximum at . (Put NA if none.)
Then $f''(x)$ =
The following questions ask for endpoints of intervals of upward and downward concavity for the function $f(x)$.
Write INF for $\infty$, MINF for $-\infty$, and put NA if there are no intervals of that type.

The interval of upward concavity for $f(x)$ is from
to
The interval of downward concavity for $f(x)$ is from
to
$f(x)$ has a point of inflection at . (Put NA if none.)