One-Sided Derivative/Examples
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Examples of One-Sided Derivatives
Absolute Value Function at $x = 0$
Let $f$ be the real function defined as:
- $\map f x = \size x$
where $\size x$ denotes the absolute value function.
Then:
\(\ds \map {f'_+} 0\) | \(=\) | \(\ds 1\) | where $\map {f'_+} 0$ denotes the right-hand derivative of $f$ at $x = 0$ | |||||||||||
\(\ds \map {f'_-} 0\) | \(=\) | \(\ds -1\) | where $\map {f'_-} 0$ denotes the left-hand derivative of $f$ at $x = 0$ |
while the derivative of $f$ at $x = 0$ does not exist.