We present a beautiful but relatively unknown theorem that every differentiable function f from a closed subset of P **R** into **R**
admits differentiable extension F:**R**-->**R**.
We present an elementary proof of this result based
on a construction sketched in a hard-to-access 1923 paper of V. Jarnik.
Using this construction, we also obtain an elegant
version of Whitney extension theorem characterizing when
such an f admits continuously differentiable extension.

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**Last modified June 6, 2017.**