What is the geometric meaning of the third derivative of a function at a point?

This question is now asked on the sister site: https://math.stackexchange.com/questions/14841/what-is-the-meaning-of-the-third-derivative-of-a-function-at-a-point. If you have an interesting answer to contribute, please do it there!

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    $\begingroup$ It is the jerk! $\endgroup$ Dec 18, 2010 at 19:14
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    $\begingroup$ I'm surprised at the claim it is not a "real" question. It is! For example see here. en.wikipedia.org/wiki/Jerk_%28physics%29 I feel this should be re-opened. $\endgroup$ Dec 18, 2010 at 20:38
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    $\begingroup$ drbobmeister, sleepless in beantown and Dick Palais: You all are right that there are plenty of great answers to this poorly phrased question. If one of you reformulates it in the form of a good question, then I'm sure everybody will support reopening it. $\endgroup$ Dec 18, 2010 at 23:17
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    $\begingroup$ Though this question does have a reasonable answer, it seems to me that it is not at the level of MO. It would be more appropriate for math.stackexchange.com. $\endgroup$ Dec 19, 2010 at 1:26
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    $\begingroup$ I asked the question over the sister site math.stackexchange.com/questions/14841/… My feeling is that (edited of course) this is a good MO question because it is certainly a question that is on the minds of many mathematicians in the context of teaching and also in some research contexts, and I am not aware of very good answers. $\endgroup$
    – Gil Kalai
    Dec 19, 2010 at 9:58