Partitions of Unity Application

If f: S --> R and f is differentiable of class C^r at each point x of S, then f may be extended to a C^r function h: A --> R that is defined on an open set A of R^n containing S.

I'm given a hint to find appropriately chosen neighbourhoods to cover S, and let A be their union, and take a C^infinity partition of unity on A dominated by this collection of neighbourhoods.

I'd appreciate any help I can get.