Relative Extrema of $|x^2 - 1|$ for $-4 \leq x \leq 4$. So the derivative is $-2x$ for $-1 \leq x \leq 1$ and $2x$ for $x \in [-4, 4] \setminus [-1, 1]$. By the Interior Extremum Theorem, there is an extremum at $ x = 0$ because the derivative exists and it's 0. What do we call $x=-1,1$? They are certainly "low" points. In spirit, they are relatively extreme, but they don't fit the definition of relative extremum (no derivative, I believe). Is there a name for them? Below is a plot, if that helps. !|x^2-1|

They are global minima.

**Definition.** Let $\Omega$ be a set and let $f \colon \Omega \to \mathbb{R}$ be a function. A point $p \in \Omega$ is a global minimum of $f$ if $f(p) \leq f(x)$ for every $x \in \Omega$.

No need to use derivatives here. But of course the whole answer is misleading and you are focusing on the lack of a tangent line at those points. If so, in italian we use the term "angular point of singularity", since the graph has a left tangent line and a right tangent line with different slopes.