In real life what does it mean? I remember d1 is the slope at a given point. D2… D3… D4 jerk? What do D5 and D6 mean? I took calc 2 in uni but I cant remember and have no idea anymore.
In: Mathematics
The first derivative is the rate of change. If you have a function that describes position, its rate of change is velocity.
The second derivative is the rate of change of the rate of change. In this case, it would be how quickly the velocity is changing, which is acceleration.
The third derivative is the rate of change of the rate of change of the rate of change. Harder to visualize, but still meaningful. Rate of change of acceleration is called jerk (or jolt), becasue that’s what you feel when you are in a vehicle that changes its rate of acceleration.
Higher-order derivatives are harder to visually and use whimsical names like jounce, flounce, snap, and yank. But that’s what math is for, way to precisely describe concepts we can’t hold in our brains all at once.
Also, derivatives don’t “start” anywhere, position is just a convenient example. Position itself is the first derivative of something called absement and the second derivative of absity.
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