$(1$ point$)$ Consider the function

$f(x)=\frac{e^x}{3+e^x}$

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

$f^{\text{'}}(x)$

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

$f^{\text{'}\text{'}}(x)=$

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