Definition:Piecewise Continuously Differentiable Function

Definition
A real function $f$ defined on a [[Definition:Closed Real Interval|closed interval] $\left[{a \,.\,.\, b}\right]$ is piecewise continuously differentiable if:


 * there exists a finite partition $P = \left\{{x_0, \ldots, x_n}\right\}$ of $\left[{a \,.\,.\, b}\right]$, $x_0 = a$ and $x_n = b$, such that $f$ is continuously differentiable on $\left({x_{i−1} \,.\,.\, x_i}\right)$ for every $i \in \left\{{1, \ldots, n}\right\}$.