Differentiability of an Absolute Value Function

$f$ is differentiable at $x = 1$.

$f$ is continuous at $x = 1$ but the left and right derivatives at $x = 1$ are not equal.

$f$ is not continuous at $x = 1$.

$\displaystyle\lim\limits_{h \to 0^-} \frac{f(1 + h) - f(1)}{h} = \lim\limits_{h \to 0^+} \frac{f(1 + h) - f(1)}{h}$