Find the interval(s) on which $f(x) = \frac{x}{x^{2} + 1}$ is strictly increasing.

Explanation

1. 01

   $f'(x) = - \frac{\left(x - 1\right) \left(x + 1\right)}{\left(x^{2} + 1\right)^{2}}$, which is 0 at $x = -1, 1$.

2. 02

   $f'(x) > 0$ on $(-1, 1)$ and $f'(x) < 0$ on $(-\infty, -1) \cup (1, \infty)$.

3. 03

   So $f$ is strictly increasing on $(-1, 1)$.