Construct indifferentiable Lipschitz function

Question

Construct a Lipschitz function on the whole real line, which is not differentiable at exactly 3 points.

Answer 1

$f(x)= \max( |x|, 1+{1 \over 2}|x|)$.

This is Lipschitz with rank one and is differentiable except at $\{ -2, 0 , 2 \}$.