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Math Help - Cubics Proof

  1. #1
    Member classicstrings's Avatar
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    Cubics Proof

    Hi!

    How would I prove that joining the maximum and mimimum of a cubic will form a line that always intersects the cubic at the middle of those two points? How do I prove it generally? Thanks!
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  2. #2
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    Quote Originally Posted by classicstrings
    Hi!

    How would I prove that joining the maximum and mimimum of a cubic will form a line that always intersects the cubic at the middle of those two points? How do I prove it generally? Thanks!
    The curve, y=x^3 got no maxima nor minima
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  3. #3
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    oops, i meant prove it for ax^3 + bx^2 + cx + d

    sorrY!
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    Quote Originally Posted by ThePerfectHacker
    The curve, y=x^3 got no maxima nor minima
    Based on this post on another site, the proof will use the local max and min. It's interesting there's nothing there about the global max/min issue.
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  5. #5
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    Quote Originally Posted by JakeD
    Based on this post on another site, the proof will use the local max and min. It's interesting there's nothing there about the global max/min issue.
    PH's point is that y=x^3 does not have local extrema.

    RonL
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