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There are several uses.

For example:

* When analyzing curves, the second derivative will tell you whether the curve is convex upwards, or convex downwards.

* The Taylor series, or MacLaurin series, lets you calculate the value of a function at any point... or at least, at any point within a given interval. This method uses ALL derivatives of a function, i.e., in principle you must be able to calculate the first derivative, the second derivative, the third derivative, etc.

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Q: What is the use of successive differentiation?
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