Category:Piecewise Continuously Differentiable Functions

This category contains results about Piecewise Continuously Differentiable Functions.
Definitions specific to this category can be found in Definitions/Piecewise Continuously Differentiable Functions.

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

$f$ is piecewise continuously differentiable if and only if

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 $\openint {x_{i - 1}} {x_i}$ for every $i \in \set {1, \ldots, n}$.