Piecewise Smooth

Definition

$C_p^{\prime }(a,b)$

function $f$ and $f^{\prime }$ are Piecewise Continuous on $(a,b)$

Facts

If $f\in C_p^{\prime }(a,b)$, then for each $x_0\in [a,b]$, $f_{+}^{\prime }(x_0)$ and $f_{-}^{\prime }(x_0)$ are exist.