Definition:Smooth Real Function

Definition

A real function is smooth if and only if it is of differentiability class $C^\infty$.

That is, if and only if it admits of continuous derivatives of all orders.

Also defined as

Some sources define a smooth function as a real function which has a continuous first derivative everywhere.

Also see

My brother Esau is an hairy man, but I am a smooth man. -- Take A Pew