# Is there any meaning to higher order derivatives?

1. Mar 4, 2013

### runningninja

We know that the first derivative represents the slope of the tangent line to a curve at any particular point. We know that the second derivative represents the concavity of the curve.
Or, the first derivative represents the rate of change of a function, and the second derivative represents the rate of change of the rate of change of a function.
So, geometrically speaking, is there any meaning to the third, fourth, fifth, or any derivative above the second?

2. Mar 4, 2013

### CompuChip

Well, of course the third derivative is the rate of change of the rate of change of the rate of change of the function, and so on.
And actually, in some cases it has a name, for example
velocity (first derivative) -> acceleration (second) -> jerk (third) -> jounce (fourth)

However, I think that if you look at physics in general, you will find remarkably few third and higher order derivatives, most processes involve first and second ones.

3. Mar 6, 2013

### Vodkacannon

Interestingly enough, if you infinitely integrate a position function, the result makes no physical sense what so ever, only the derivation does. The derivation converts the units that CompuChip mentioned.