What happens when you find the derivative of $f(x) =|x^2-1|$. Let $f(x) =|x^2-1|$.
I'm trying to see if this function has a point of inflection and even though looking at the graph tells me the answer already, I was just curious.
What happens to the modulus part when you differentiate it? Would you just take the piecewise version of the function and differentiate each function?

$$\dfrac{\text{d}}{\text{d}x} \vert f(x)\vert = f'(x) \text{sgn}(f(x))$$
Where $\text{sgn}(\cdot)$ is the signum function.
$$\text{sgn}(f(x)) = \dfrac{\vert f(x) \vert}{f(x)}$$
