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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???

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  1. amistre64
    • 2 years ago
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    f''' is acceleration, and f'''' is called a jerk; the speed at which the acceleration is changing

  2. amistre64
    • 2 years ago
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    all the derivatives combined tell us how a function is moving at a single point

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

  4. amistre64
    • 2 years ago
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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

  5. robinfr93
    • 2 years ago
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    I don't wanna know it what it means in terms of distance travelled.. Just in general term..

  6. terenzreignz
    • 2 years ago
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    hey @amistre64 I think it's the third derivative that's the jerk?

  7. amistre64
    • 2 years ago
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    maybe, i lost count after 1.5

  8. robinfr93
    • 2 years ago
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    yah its the third derivative..

  9. terenzreignz
    • 2 years ago
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    LOL Unless f' is the position function and f is... some function whose derivative is the position function XD

  10. robinfr93
    • 2 years ago
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    Welllllllll... So can anybody answer my question?? Please??

  11. terenzreignz
    • 2 years ago
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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

  12. amistre64
    • 2 years ago
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    "all the derivatives combined tell us how a function is moving at a single point" by, amistre64

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

  14. terenzreignz
    • 2 years ago
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    yayz :D

  15. TuringTest
    • 2 years ago
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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.

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

  17. robinfr93
    • 2 years ago
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    That just prove sine function is an oscillating function.. nonetheless thank you to all!! :P

  18. robinfr93
    • 2 years ago
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    @amistre64 Though if I missed something in your post, Do point out..

  19. amistre64
    • 2 years ago
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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

  20. robinfr93
    • 2 years ago
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    :D A very good point Indeed!!

  21. amistre64
    • 2 years ago
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    good luck ;)

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