# Definition:Differentiable Mapping/Real Function/Point/Definition 2

Let $f$ be a real function defined on an open interval $\left({a \,.\,.\, b}\right)$.
Let $\xi$ be a point in $\left({a \,.\,.\, b}\right)$.
$f$ is differentiable at the point $\xi$ if and only if the limit:
$\displaystyle \lim_{h \to 0} \frac {f \left({\xi + h}\right) - f \left({\xi}\right)} h$