# Higher Derivatives

dekoi
This question is more theory than anything else.

I am given the graph attached:

This graph shows four functions.
1.) Position function of a car. ($$f(x)$$)
2.) Velocity of the car. ($$f'(x)$$)
3.) Acceleration of the car. ($$f''(x)$$)
4.) Jerk of the car. ($$f'''(x)$$)

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.

#### Attachments

• calculusss.jpg
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