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Math Help - Very quick conceptual point of inflection idea

  1. #1
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    Very quick conceptual point of inflection idea

    When you have f'(x) = 0 and f''(x) = 0 for the same x, is it both a point of inflection and a max/min or just a max/min? I think it's only a max or min right? And x is not a point of inflection for f.
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  2. #2
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    Consider f(x)=x^3 at x=0.
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  3. #3
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    Do you mean there is a function where f"(c)=0 and f'(c)=0 but (1) is not a point of inflection, but is a max/min? or a point where both equal 0 and (2) there is a point of inflection and a max/min? or (3) there is point of inflection but no max/min.

    (1) i can not seem to find an example for this but it does seem entirely possible

    (2) in order for this situation to occur f(x) must come to a point, c, where the slope changes from increasing to decreasing, or vice-versa, and from concave up to concave down, or vice versa. In order for all this to happen at the point c, f must come to a sharp point. If f comes to a sharp point it is not differentiable. Thus the second is not a possibility.

    (3) example of x^3 at x=0
    Last edited by Hellweg; May 4th 2010 at 05:32 PM.
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