Is there any geometrical meaning for the $n\text{th}$ derivative of a function (like a first derivative gives slope, a second derivative gives concavity)?
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Well, the second derivative also gives the slope of the first derivative, and so on. In general, the more derivatives you have at some point $x_0$, the smoother is the function at $x_0$. I don't think there is much else you can say. – Manolito Pérez Dec 31 '17 at 20:13
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Related: How are the higher derivatives (jerk, jounce) of position with respect to time used in physics? AND What is the meaning of the third derivative of a function at a point AND – Dave L. Renfro Dec 31 '17 at 21:14
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What is an example of an application of a higher order derivative ($y^{(n)}$, $n\geq 4$)? AND Meaning of different Orders of Derivative AND Non-physical Jounce Examples in Nature AND – Dave L. Renfro Dec 31 '17 at 21:14
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What are the derivatives of position with respect to time AND these physics stack exchange questions – Dave L. Renfro Dec 31 '17 at 21:15
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You may use physical analogies to aid your understanding. The first derivative at a point is the slope of the tangent line to the graph of the function at that point, while the second derivative measures the 'velocity' of the slope (think of the independent variable as time), the third would then be the 'acceleration' of slope, the third jerk, the fourth jounce, and higher derivatives are just rates of rates of rates of rates of... the slope
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