#### OldManMath

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- Thread starter OldManMath
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Every time you get in your car, you witness differentiation first hand. Your speed is the first derivative of your position. And when you step on the accelerator or the brake — accelerating or decelerating — you experience a second derivative. If a function gives the position of something as a...

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-Dan

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The second derivative can tell us exactly the same kinds of things about the first derivative, that the first derivative tells us about the original function.

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As topsquark pointed out, the 2nd derivative of the position function is the acceleration function. Also, the 2nd derivative of the velocity function is what is known as the jerk function. This is the derivative of the acceleration function, that it it is the instantaneous change in the acceleration wrt time.

That is all physics. Just talking math, the 2nd derivative of f(x) talks about the concavity of f(x) which helps draw a pretty accurate graph of f(x).

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Suppose a particle is moving on a path described by y = f(x).

Then the second derivative [w.r.t. x which is f"(x)] can be used to calculate the radius of the path (think about motors running on "oval" path in a race-way).

Previous posts told you how second derivative can be used to calculate acceleration. That in conjunction with the 2nd law of motion (Newton) can be used to calculate the force needed to move the particle with that acceleration.