Higher Derivatives

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Hook

Velocity, acceleration, and jerk

If the derivative is speed, the derivative of the derivative is acceleration. You can keep going — jerk (3rd), snap (4th). Each derivative is the rate of change of the last, and the second derivative reveals the SHAPE of the graph: concavity, inflection. The bend of a curve is hiding in f''.

f' = velocity, f'' = acceleration. The sign of f'' is the concavity.

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