# If $f''(x)=0$ but is not an inflection point, what is it called?

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?

• A critical point of the derivative. (No, it doesn't have any specific name). – Arturo Magidin Oct 21 '11 at 20:17
• @ArturoMagidin Okay, thanks! – martias Oct 22 '11 at 16:19
• @Arturo: Perhaps you should make that an answer? – davidlowryduda Oct 23 '11 at 6:42