Why the interpolation polynomials for $f=|x|,x\in[-1,1]$ will oscillate near the endpoint of $[-1,1]$ as $n$ increases?
I know that one explanation of the Runge's phenomenon is that the interpolation error is not bounded which make use of the derivates of $f$.Wiki Runge's phenomenon
However, when $f=|x|$, it is not in differentiable at $x=0$. So, how to understand why the interpolation polynomials oscillate near $x=1$ and $x=-1$?