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Prove that the the function $f(x) = |x-1|+|x-2|$ is not differentiable at $x = 1$,and $x = 2$.

This is actually an objective type question where there is $3$ other options $(\{0\},\{1\},\{3\},\{1,2\})$,now the problem is graph is not really much of a choice,hence I guess I have to break the functions into ranges and then solve, any idea ?

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