Nonnegative Whitney Extension Problem for $C^1(\mathbb{R}^n)$

Let $f$ be a real-valued function on a compact subset in $\mathbb{R}^n$. We show how to decide if $f$ extends to a nonnegative and $C^1$ function on $\mathbb{R}^n$. There has been no known result for nonnegative $C^m$ extension from a general compact set $E$ when $m > 0$. The nonnegative extension problem for $m \geq 2$ remains open.