Q:

Function that visually looks smooth but is not

I am wondering how closely our intuition for "smooth" aligns with the mathematical definition of smooth. To that end I was wondering if there is any function that looks "smooth" (i.e. could reasonably be called "smooth" by even a non-mathematical person at any scale) but is not infinitely differentiable (smooth). 

A:

For instance, $f(x) = |x|^3$ looks smooth but has no 3rd derivative.

