  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.
