- #1

- 113

- 1

The second derivative represents the concavity of the function's curve.

However I am unable to figure out what the other derivatives of a function represent either physically or geometrically.

Pleae help.

- Thread starter AlbertEinstein
- Start date

- #1

- 113

- 1

The second derivative represents the concavity of the function's curve.

However I am unable to figure out what the other derivatives of a function represent either physically or geometrically.

Pleae help.

- #2

quasar987

Science Advisor

Homework Helper

Gold Member

- 4,783

- 15

That's as deep as I can get. I don't know what that says about the geometry of the curve.

- #3

StatusX

Homework Helper

- 2,564

- 1

- #4

- 38

- 0

Hmm... did not know that there was a 3rd dirivative. Guess your learn something new every day!

- #5

- 506

- 1

Sometimes the second derivative yields no information about concavity. Consider the two different functions f(x) = x^4 and g(x) = -x^4. These two functions have different concavities, but if evaluated at (0, 0), their second derivative is the same. A higher derivative will reveal their different orientations at (0, 0).

Physically, the name "jerk" is given to the third derivative of a position function with respect to time. There are standardized limits placed on jerk for things as simple as starting and stopping trains. Limits are placed on much higher derivatives for sensitive instruments like the Hubble telescope. Very few people have deemed it necessary to give names to these quantities beyond fourth derivative, fifth derivative and so on.

Physically, the name "jerk" is given to the third derivative of a position function with respect to time. There are standardized limits placed on jerk for things as simple as starting and stopping trains. Limits are placed on much higher derivatives for sensitive instruments like the Hubble telescope. Very few people have deemed it necessary to give names to these quantities beyond fourth derivative, fifth derivative and so on.

Last edited:

- Last Post

- Replies
- 13

- Views
- 3K

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 770

- Replies
- 6

- Views
- 2K

- Last Post

- Replies
- 5

- Views
- 1K

- Last Post

- Replies
- 3

- Views
- 15K

- Last Post

- Replies
- 4

- Views
- 9K

- Last Post

- Replies
- 1

- Views
- 843