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Thread: Inflexion point

  1. #1
    Newbie
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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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    A necessary condition for $\displaystyle x$ to be an inflection point is that $\displaystyle f''(x)=0$

    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 $\displaystyle f'(x)$ and notice that it does not change sign anywhere.
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