Limits Continuity And Differentiability

The function $f$ is NOT differentiable at $x = 0$

There is a positive real number $\delta$, such that $f$ is a decreasing function on the interval $(0, \delta)$

For any positive real number $\delta$, the function $f$ is NOT an increasing function on the interval $(-\delta, 0)$

$x = 0$ is a point of local minima of $f$