What is the Practical Application of the 7th Derivative in the Real World?

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The seventh derivative of a position function is known as "snap" or "jounce," representing the change in acceleration over time. Unlike the first three derivatives, which have clear physical interpretations, higher-order derivatives like snap are less commonly applied in practical scenarios. They find their primary use in theoretical contexts, particularly in physics and engineering calculations. Additionally, snap can aid in analyzing complex systems, including robotics, control systems, and financial models. While its real-world applications are limited, snap remains a valuable concept in advanced mathematical analysis.
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What is the name of the seventh derivative of a position function? I know the first derivative is velocity and the second is acceleration, and the third is jerk. But what is the realworld use of a 7th derivative??
 
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I don't believe it has any special name.
 


The seventh derivative of a position function is called "snap" or "jounce." This is a measure of the change in acceleration over time. While the first three derivatives (velocity, acceleration, and jerk) have direct physical interpretations and applications, the higher order derivatives (such as snap) have less practical uses in the real world. They are typically used in mathematical and theoretical contexts, such as in physics and engineering calculations. However, they can also be used to analyze and evaluate the behavior and performance of complex systems, such as in robotics, control systems, and financial models. Overall, the seventh derivative may not have a direct real-world application, but it is a valuable tool in advanced mathematical analyses and models.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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