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.

For the following questions, write

You can earn partial credit on this problem.