Definition:Piecewise Continuously Differentiable Function/Definition 2

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Definition

Let $f$ be a real function defined on a closed interval $\left[{a \,.\,.\, b}\right]$.


$f$ is piecewise continuously differentiable if and only if:

there exists a finite subdivision $\left\{{x_0, \ldots, x_n}\right\}$ of $\left[{a \,.\,.\, b}\right]$, $x_0 = a$ and $x_n = b$, such that:
$f$ is continuously differentiable on $\left[{x_{i−1} \,.\,.\, x_i}\right]$, the derivative at $x_{i−1}$ understood as right-handed and the derivative at $x_i$ understood as left-handed, for every $i \in \left\{{1, \ldots, n}\right\}$.



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