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

The critical numbers are $- 1$ and $1$ where $f ' \left(x\right)$ does not exist.
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 $\left(- 1 , 0\right)$ and $\left(1 , 0\right)$.
Note that $f \left(x\right) \ge 0$ for all $x$.
Both $f \left(- 1\right)$ and $f \left(1\right)$ are $0$, so both are locations of the absolute minimum.