Question

Question #39963

Answer 1

It is not differentiable at `x=2`.

Explanation:

The graph of `f(x) = abs(x-2)` is th graph of `y=absx` translated 2 to the right.

`f(x) = abs(x-2)`
graph{abs(x-2) [-3.54, 7.56, -2.043, 3.506]}

As you can see, there is a corner point (a cusp) at `x=2` so the function is not differentiable there.