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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 $X$.

flonk
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2 Answers2

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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."

Community
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Ilmari Karonen
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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.

Najib Idrissi
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  • The phrase is not my problem, just an illustration. I really need a handy word for the point, like it also exists in other contexts, e.g., the root $x_0$ or the jump $x_0$ . This is not satisfying, but I think something like tangent-jump, but less ugly :) – flonk Dec 19 '14 at 10:05
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    Why do you "really need" such a handy word? – Najib Idrissi Dec 19 '14 at 10:05
  • As I said, because always using the point where $f$ is continuous but not smooth in longer sentences, where this is merely a side-fact, disctracts from the main statement. It is matter of language. As when you say the root $x_0$ this is short enough to not distract the reader from the statement about the root. – flonk Dec 19 '14 at 10:07
  • maybe: $x_0$ is a $continuity-only$ point (''only'' is to mention that there is no more smoothness) – Idris Addou Dec 19 '14 at 12:00