# The third derivative.

1. May 25, 2013

### NATURE.M

Does the third derivative have any physical significance in relation to the original function?
For instance, the first derivative is the slope function (and can be used to find the local max/min). And the second derivative demonstrates the concavity/curvature of the original function (or the rate at which the slope changes).

2. May 25, 2013

### lugita15

Here's an old post of mine that may help answer your question:

3. May 25, 2013

### SteamKing

Staff Emeritus
In kinematics, the third derivative of the position function represents the "jerk".

4. May 27, 2013

### NATURE.M

Okay, I've heard the term jerk before used in a physics context, although it rarely (if ever) shows up in Physics Textbooks.

5. May 27, 2013

### SteamKing

Staff Emeritus
Things like 'jerk' and 'jounce' find application in some specialized areas of physics and engineering:
http://en.wikipedia.org/wiki/Jerk_(physics)

For a general introduction to physics, velocity and acceleration are more commonly encountered.

6. May 28, 2013

### cosmik debris

Jerk and its higher orders are used in the design of camshafts where higher derivatives of position are optimised to keep mechanical stresses and strains within bounds, whilst providing the largest area under the curve. e.g. in a combustion engine you want to lift the valve as quickly as possible and keep it open as long as possible etc.