From: Dick Buck
To: Teacher2Teacher Public Discussion
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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