Intervals of Increase and Decrease?

Question

Let f(x) = e^x / (8+(e^x))

then f'(x) = 8e^x / ((8+(e^x))^2)

In what intervals is f increasing and decreasing ?

And what are the local max and min (if they exist) ?

Answer 1

Since e^x is never 0, f' is never 0. So there are no local minima or maxima. So f is monotonic. Evaluate f at two different values of x, see if it's increasing or decreasing, and you're done.