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(Originally asked on MO by AJAY.)

What is the geometric, physical, or other meaning of the third derivative of a function at a point?

If you have interesting things to say about the meaning of the first and second derivatives, please do so.

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    Please see [this](http://dx.doi.org/10.1119/1.11504) and [this](http://www.jstor.org/stable/2690245); those two articles are where I picked up my intuition for the third derivative.2010-12-19
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    @J.M.: That's great; I think you should make it an answer.2010-12-19
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    Too short for an answer: I like to think about third derivative as telling me how quickly the curvature is changing. Third derivatives also give us "osculating cubics" (for when osculating quadrics just won't do).2012-05-02
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    I thought that DOIs were meant to be permanent and resilient against location changes, but the first in @J.M.'s link seems to have succumbed to AIP reorganisation. As best I can tell, it pointed to [Schot, "Jerk: The time rate of change of acceleration", Am. J. Phys. 46, 1090 (1978)](http://scitation.aip.org/content/aapt/journal/ajp/46/11/10.1119/1.11504). (In case the JStor link suffers a similar fate, it points to another article by the same author: [Schot, "Aberrancy: Geometry of the third derivative", Mag. Mag. 51, no. 5 (Nov. 1978), pp. 259–275](http://www.jstor.org/stable/2690245).)2016-11-23

9 Answers 9