I am new to calculus and currently learning differentiation. I understood that the first derivative indicates the slope of the function and the second derivative indicates the rate at which the slope is increasing or decreasing. I have seen some questions asking to find the 3rd derivative of functions and can't understand what would be its geometrical/physical significance. I would appreciate if someone could explain why 3rd derivatives are important. Thanks in advance :)
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Jean-Claude Arbaut
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Aniket Gupta
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2This quantity is called "jerk". You can think of it as the rate at which acceleration changes. If your function measures position after time $t$, then the first derivative measures speed, the second measures acceleration, and the third measures the rate of change of acceleration. – wormram Apr 27 '20 at 07:25
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For more details and applications see here. – wormram Apr 27 '20 at 07:27
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@Sunyata Thanks, I understood – Aniket Gupta Apr 27 '20 at 08:32
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It may be worth asking on PSE. It may have been asked before, there is even a specific tag. – Jean-Claude Arbaut Apr 27 '20 at 09:30