## robinfr93 2 years ago Ummmm.. Just Curious.. But what does a triple and quadruple differenciation of a function signify graphically?? I know its increasing or decreasing with first derivative, second tells concavity that means how much.. But whats the role of 3rd and 4th???

1. amistre64

f''' is acceleration, and f'''' is called a jerk; the speed at which the acceleration is changing

2. amistre64

all the derivatives combined tell us how a function is moving at a single point

3. ParthKohli

$$f'''$$ is a jerk? I think I am the $$f'''$$ you are looking for :-)

4. amistre64

spose you wanted to create a polynomial that moved like the sine function both functions would have to MOVE in the same manner, and all of their derivaties would have to be equal

5. robinfr93

I don't wanna know it what it means in terms of distance travelled.. Just in general term..

6. terenzreignz

hey @amistre64 I think it's the third derivative that's the jerk?

7. amistre64

maybe, i lost count after 1.5

8. robinfr93

yah its the third derivative..

9. terenzreignz

LOL Unless f' is the position function and f is... some function whose derivative is the position function XD

10. robinfr93

11. terenzreignz

Well... f'(c) is the slope of the tangent line at the point x = c f''(c) is the concavity of the graph at the point x = c f'''(c) is the rate of change of the concavity??? XD

12. amistre64

"all the derivatives combined tell us how a function is moving at a single point" by, amistre64

13. robinfr93

@terenzreignz As much of a guess that was it actually is the right answer!! :D :P

14. terenzreignz

yayz :D

15. TuringTest

concavity is the rate change of the slope, so all that is saying is the rate change of the rate change of the slope, which we can extend to all derivatives.

16. amistre64

sin(0) = 0 ; P(x) = 0 sin'(0) = 1 ; P(x) = 0 + x sin''(0) = 0 ; P(x) = 0 + x +0x^2/2! sin'''(0) = -1 ; P(x) = 0 + x +0x^2/2! -x^3/3! sin(x) = P(x)= $$\Large\sum_{n=0}^{\inf}\frac{(-1)^n}{(2n+1)!}x^{2n+1}$$

17. robinfr93

That just prove sine function is an oscillating function.. nonetheless thank you to all!! :P

18. robinfr93

@amistre64 Though if I missed something in your post, Do point out..

19. amistre64

i was just demonstrating that the successive derivatives of a function define how it is moving at a single point, and that 2 function that are equal at a single point, and equal at all their successive derivatives are the same at that point. Since polynomials are so much easier to play with, if we can construct a polynomial to work from, that converges (is the same), at a point or range of points. Then mathing is so much simpler

20. robinfr93

:D A very good point Indeed!!

21. amistre64

good luck ;)