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## robinfr93 Group Title 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??? one year ago one year ago

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1. amistre64 Group Title

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

2. amistre64 Group Title

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

3. ParthKohli Group Title

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

4. amistre64 Group Title

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 Group Title

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

6. terenzreignz Group Title

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

7. amistre64 Group Title

maybe, i lost count after 1.5

8. robinfr93 Group Title

yah its the third derivative..

9. terenzreignz Group Title

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

10. robinfr93 Group Title

Welllllllll... So can anybody answer my question?? Please??

11. terenzreignz Group Title

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 Group Title

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

13. robinfr93 Group Title

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

14. terenzreignz Group Title

yayz :D

15. TuringTest Group Title

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 Group Title

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 Group Title

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

18. robinfr93 Group Title

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

19. amistre64 Group Title

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 Group Title

:D A very good point Indeed!!

21. amistre64 Group Title

good luck ;)