Consider the function $$f(x)=\frac{e^x}{4 + e^x}$$

Note: Below, use interval notation for intervals or sets of points on the x-axis.

$f'(x)$ =
The open interval of increase for $f(x)$ is
The open interval of decrease for $f(x)$ is
$f(x)$ has a local minimum at each point $x$ in this set
$f(x)$ has a local maximum at each point $x$ in this set
$f''(x)$ =

The open interval of upward concavity for $f(x)$ is
The open interval of downward concavity for $f(x)$ is
$f(x)$ has a point of inflection at each point $x$ in this set