A question that is often asked in Extension Theory is the following: Given $E \subset \mathbb{R}^n$, and $f:E \rightarrow \mathbb{R}$. Is it possible to extend $f$ to a function lying in the space $X(\mathbb{R}^n)$ ?. This question has been answered in the case when $X$ is the space $C^m$ of functions continuously differentiable through order $m$. I will prove the relevant theorem in the special case $m=2$ for finite sets $E$, and time permitting discuss some other interesting variants.