Consider the function $\displaystyle f(x) = e^{arctan(2x)} $

1. Find the horizontal asymptotes of the function.

2. State the interval(s) where the function is increasing.

3. Find the inflection point.

4. Find the intervals where the graph is concave up and concave down.

It appears I've ran into a problem here. All I could do on my own so far was find f'(x):

$\displaystyle f'(x) = e^{arctan(2x)}(\frac{2}{1+4x^2}) = \frac{2e^{arctan(2x)}}{1+4x^2} $

Setting this equal to 0, $\displaystyle e^{arctan(2x)} = 0$ which has no solution? Doesn't look quite right to me.