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If the second derivative of a function $f(x)$ equals zero at point $x_0$ ( $f''(x_0)=0$ ), the point is an inflection point if the concavity changes. Here's an example of an inflection point.

If the concavity does not change, what is the point called? Does it have any specific name?

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    $\begingroup$ A critical point of the derivative. (No, it doesn't have any specific name). $\endgroup$ – Arturo Magidin Oct 21 '11 at 20:17
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    $\begingroup$ @ArturoMagidin Okay, thanks! $\endgroup$ – martias Oct 22 '11 at 16:19
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    $\begingroup$ @Arturo: Perhaps you should make that an answer? $\endgroup$ – davidlowryduda Oct 23 '11 at 6:42
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It is called an undulation point. (See http://en.wikipedia.org/wiki/Inflection_point.)

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(Made into an answer so the question doesn't go without one).

The point does not have any specific name that denotes the fact that it is not a point of inflection. Of course, it is still a critical point of the derivative (one which is not a local extreme of the derivative).

So, no, it does not have a specific name.

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