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Math Help - point of inflection? confused

  1. #1
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    point of inflection? confused

    hello im having trouble with understanding the point of inflection, in my math text book using the first derivative i found out that the stationary point both have a gradient less than zero on both of its side which is a point of inflection property, however some people say that to find the point of inflection you use the 2nd derivative and see how concavity changes, this is the point i get confused on... you can see the whole problem in the pictures below...

    can you identify a point of inflection using the first derivative?

    please explain it step by step because im very confused on this part...


    point of inflection? confused-question-begining-answer.jpgpoint of inflection? confused-rest-answer.jpg

    thank you in advance
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  2. #2
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    Re: point of inflection? confused

    There is a difference between an inflection point and an extremum.

    Don't quote me on the exact definitions, but I can tell you the general idea. An extremum is when a function has a maximum or minimum value. This happens because the derivative changes sign, because that in turn means that the function switched from rising to falling or vice versa, creating a "hill." If the function is differentiable, the derivative at an extremum will be 0, but the converse (vice versa) won't necessarily hold, because of the example in your book.

    An inflection point is when the second derivative (the derivative of the derivative) changes sign. So if the second derivative exists at that point, it will be equal to 0. This is the point where the concavity of the function changes.
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  3. #3
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    Re: point of inflection? confused

    oooh now i get it thanks a lot appretiate ur help
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