Is there a good short phrase for a point where a function is continuous but not smooth?

Question

Given a point $x_0$ where a function $f$ is $C^0$ but not $C^1$, how could one call this point intuitively?

I am not looking for a technically precise term (like a point where $f'$ is discontinuous), but rather a descriptive and short phrase. I need to write a longer text, where I want to use it to remind the reader of this property, think of sentences like Condition $Y$ ensures the ??-point $x_0$ of $f$ to fulfil $X$.

Answer 1

The word I've most commonly seen used for a point at which a function is continuous but not differentiable is "kink", as in:

"The function $f(x) = |x|$ has a kink at the origin."

Answer 2

No, there is no such phrase. Simply reword your sentence: "Condition $Y$ ensure that $f$ is continuous but not smooth at $x_0$, which makes it fulfill $X$". No need for arcane terminology here.