Consider $f(x)=\mid x\mid$

This function is continuous everywhere but it is not differentiable at $x=1$.

Hence the combined function $f(x)=\mid x\mid+\mid x-1\mid$ is continuous everywhere but not differentiable at exactly $0$ and $1$.

Hence an example of a function which is continuous everywhere but fails to be differentiable exactly at two points is $\mid x\mid,\mid x-1\mid$