Question

What are the values and types of the critical points, if any, of `f(x) = abs(x^2-1)`?

Answer 1

The critical numbers are `-1` and `1` where `f'(x)` does not exist.

Explanation:

Depending on the terminology you are using that might make the critical points `-1` and `1`, or you might have been taught to say they are `(-1,0)` and `(1,0)`.

Note that `f(x) >=0` for all `x`.

Both `f(-1)` and `f(1)` are `0`, so both are locations of the absolute minimum.