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I was looking for the name given to the more locally convex / concave points of a given function $f(x)$ for instance, the ones I have marked in the multiplicative inverse function below. In the case of the multiplicative inverse it might be also a fixed point, but being a fixed point does not necessarily mean that is also locally the most convex / concave point. It is not an inflection point as well, and I am not sure if it is an stationary point, because the position is not a local maximum or minimum. So is there a name for the most locally convex / concave points of a function? thank you.

multiplicative inverse

The Wiki articles are not very clear about it:

http://en.wikipedia.org/wiki/Convex_function

http://en.wikipedia.org/wiki/Concave_function

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The word for the measure you're looking at is "curvature". I'd probably call the thing you're looking for "the point of maximum curvature"; there may be a better name but I don't know it.

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  • $\begingroup$ thank you!! so it is the point of maximum curvature. $\endgroup$ – iadvd Apr 3 '15 at 3:45

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