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Math Help - Critical Points

  1. #1
    Senior Member slevvio's Avatar
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    Critical Points

    say we have a polynomial function

    x^4+ux^2 + v x (u,v some numbers)

    does anyone know why adding a higher order term to this will not change what happens near zero (in terms of critical points near zero)
    Last edited by slevvio; August 20th 2010 at 11:21 AM. Reason: hit submit too early
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  2. #2
    MHF Contributor
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    Quote Originally Posted by slevvio View Post
    say we have a polynomial function

    x^4+ux^2 + v x (u,v some numbers)

    does anyone know why adding a higher order term to this will not change what happens near zero (in terms of critical points near zero)
    If the function had an x^5 term, the derivative of that is 5x^4.

    For very small values of x, 5x^4 will be very small... 5(0.1)^4=0.0005

    hence there will be only very small changes in the derivative near x=0, if a higher-power term is added to the function
    (depending on the proximity of x to zero).
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