One-Sided Derivative/Examples/Absolute Value Function at Zero

Examples of One-Sided Derivatives
Let $f$ be the real function defined as:
 * $\map f x = \size x$

where $\size x$ denotes the absolute value function.

Then:

while the derivative of $f$ at $x = 0$ does not exist.

Proof
Demonstrated in Derivative of Absolute Value Function.