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Math Help - Inflexion point

  1. #1
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    May 2009
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    Inflexion point

    How do I prove this?

    Prove that curve
    y=x^3+4x

    Has one point of inflexion, but no tuning points.
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  2. #2
    Senior Member Spec's Avatar
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    Aug 2007
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    A necessary condition for x to be an inflection point is that f''(x)=0

    Since there's only one solution to this equation for this function, there is at most one inflection point.

    To prove that there's no turning point, study f'(x) and notice that it does not change sign anywhere.
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