  For $k\in \N\cup \{\infty\}$ and $U$ open in $ \R$, let $\C^{\,k}(U)$ be the
ring of real valued functions on $U$ with the first $k$ derivatives continuous.
It is shown for $f\in \C^{\,k}(U)$ there is $g\in \ck{\infty}$ with $U\sbq \coz
g$ and $h\in \ck{k}$ with $fg\res_U=h\res_U$. The function $f$ and its $k$
derivatives are not assumed to be bounded on $U$. The function $g$ is
constructed using splines based on the Mollifier function. Some consequences
about the ring $\ck{k}$ are deduced from this, in particular that $\qcl(\ck{k})
= \text{Q}(\ck{k})$.
