# The Third Derivative

1. Jul 30, 2007

### x2thay

2. Jul 30, 2007

### nealh149

It's the rate of change of the slope of the first graph.

3. Jul 30, 2007

### sutupidmath

Or for example when we want to find a functions maxima or minima, or to determine the convexity of a function. FOr example if f'=f''=0 then if f''' is different from zero the function has a minima of maxima depending on the sign of the f'''.

4. Jul 30, 2007

### nicktacik

Here's a neat example. Suppose when driving a car, the car's acceleration is proportional to the position of your foot on the pedal. Now if your foot is moving with some velocity, then the third derivative of the car's motion is proportional to the velocity of your foot. And if your foot is moving with some acceleration the then the 4th derivative of the car's motion is proportional to the acceleration of your foot.

The third derivative (the jerk) has some other important implications in physics and engineering.
http://en.wikipedia.org/wiki/Jerk

5. Jul 30, 2007

### arildno

It's the third derivative of a function.
That's its "meaning".

In some approximative schemes of differential equations, it can be advantageous to express one of the unkown functions in terms of the derivatives of another unkown, thereby reducing the number of unkown functions to be found by increasing the order of the resulting diff.eq(s).
Thereby, third-and higher order derivatives may enter in the diff.eq, even if it starts out like at most a second-order problem like Newton's F=ma

The Boussinesq equation types in fluid mechanics are examples of that.

6. Nov 2, 2007

### limkimchhun

Could anyone tell me more detail about third derivative of distance and of others? What does it use for? What about fourth derivative, 5th...?
And my 2nd question is: a mouvement of a object notice by this system equation: x(t)=vxt+x0, y(t)=vy.t+y0, z(t)=vz.t+z0. What is the equation of trajectory, f(x,y,z)=?