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Q&A #3922

Teachers' Lounge Discussion: Third derivative

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From: Dick Buck <rabuck34@hotmail.com>
To: Teacher2Teacher Public Discussion
Date: 2001052509:49:04
Subject: Re: 3rd derivative

In general terms, the third derivative is just that, the derivative of
the second derivative.  If you are thinking of derivatives wrt time,
then you could picture it as the rate of change of the acceleration. 
If you are thinking of derivatives wrt "x" (the independent variable
of the system in which you are operating) then you could picture it as
the change in the concavity of the graph of "y" vs "x."  It all
depends on your frame of reference.  It has applications in many
senses.  For example, in analysis, if the second derivative of a class
C1 function equals zero and the third derivative does not equal zero
at a point on the graph of the function, then there is a POI at that
point.  In algebra, a second degree polynomial is a function whose
third derivative is identically zero, etc.


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