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

    • one year ago
  2. amistre64 Group Title
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    all the derivatives combined tell us how a function is moving at a single point

    • one year ago
  3. ParthKohli Group Title
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    \(f'''\) is a jerk? I think I am the \(f'''\) you are looking for :-)

    • one year ago
  4. amistre64 Group Title
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    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

    • one year ago
  5. robinfr93 Group Title
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    I don't wanna know it what it means in terms of distance travelled.. Just in general term..

    • one year ago
  6. terenzreignz Group Title
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    hey @amistre64 I think it's the third derivative that's the jerk?

    • one year ago
  7. amistre64 Group Title
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    maybe, i lost count after 1.5

    • one year ago
  8. robinfr93 Group Title
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    yah its the third derivative..

    • one year ago
  9. terenzreignz Group Title
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    LOL Unless f' is the position function and f is... some function whose derivative is the position function XD

    • one year ago
  10. robinfr93 Group Title
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    Welllllllll... So can anybody answer my question?? Please??

    • one year ago
  11. terenzreignz Group Title
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    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

    • one year ago
  12. amistre64 Group Title
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    "all the derivatives combined tell us how a function is moving at a single point" by, amistre64

    • one year ago
  13. robinfr93 Group Title
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    @terenzreignz As much of a guess that was it actually is the right answer!! :D :P

    • one year ago
  14. terenzreignz Group Title
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    yayz :D

    • one year ago
  15. TuringTest Group Title
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    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.

    • one year ago
  16. amistre64 Group Title
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    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)= \(\Large\sum_{n=0}^{\inf}\frac{(-1)^n}{(2n+1)!}x^{2n+1}\)

    • one year ago
  17. robinfr93 Group Title
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    That just prove sine function is an oscillating function.. nonetheless thank you to all!! :P

    • one year ago
  18. robinfr93 Group Title
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    @amistre64 Though if I missed something in your post, Do point out..

    • one year ago
  19. amistre64 Group Title
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    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

    • one year ago
  20. robinfr93 Group Title
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    :D A very good point Indeed!!

    • one year ago
  21. amistre64 Group Title
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    good luck ;)

    • one year ago
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