This question is more theory than anything else.(adsbygoogle = window.adsbygoogle || []).push({});

I am given the graph attached:

This graph shows four functions.

1.) Position function of a car. ([tex]f(x)[/tex])

2.) Velocity of the car. ([tex]f'(x)[/tex])

3.) Acceleration of the car. ([tex]f''(x)[/tex])

4.) Jerk of the car. ([tex]f'''(x)[/tex])

I have to identify which graph is which (out of a, b, c, & d), and explain why this is so.

However, I have no idea how to do this.

I am assuming that the order is A, B, C, then D. However, this is based solely on observing the shapes of the graphs (since higher derivatives become more linear), but I do not know the theory to explain this.

Any input is greatly appreciated. Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Higher Derivatives

**Physics Forums | Science Articles, Homework Help, Discussion**