Definition:Piecewise Continuously Differentiable Function/Definition 2

Definition
Let $f$ be a real function defined on a closed interval $\closedint a b$.

$f$ is piecewise continuously differentiable :


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

Also see

 * Piecewise Continuously Differentiable Function/Definition 2 is Continuous