Consider the function $f(x)=\displaystyle \frac{e^x}{4 + e^x}$. Compute the derivative of this function.

$f'(x)$ =

For the following questions, write inf for $\infty$, -inf for $-\infty$, and NA (ie. not applicable) if no such answer exists.

a.) $f(x$ is increasing on the region .

b.) $f(x)$ is decreasing on the region .

c.) $f(x)$ has a local minimum at .

d.) $f(x)$ has a local maximum at .

e.) $f''(x)$ =

f.) $f(x)$ is concave up on the region

g.) $f(x)$ concave down on the region .

h.) $f(x)$ has a point of inflection at .

Note: Many of your answers must be given in interval notation.