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 $\displaystyle f(x) = 2x^2$ and $\displaystyle g(x) = 4x^2$ of continuity $\displaystyle C^n$ over an interval $\displaystyle [0,4]$. 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($\displaystyle f(x)$ or $\displaystyle g(x)$) is the smoothest over the given interval?