According to the definition of Smooth function - Wikipedia, the free encyclopedia:

Functions that have derivatives of all orders are calledsmooth.

Suppose I've two different functions and of continuity over an interval . Because both of these functions has derivatives of all order these two functions are smooth.

What I like to know is which one of these two are smoothest?

Is it possible to kindly help me detect which function( or ) is the smoothest over the given interval?