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Math Help - Please check if I drew graph correctly?

  1. #1
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    Post Please check if I drew graph correctly?

    I wrote it by hand and this is just a rough sketch, but I'm just wondering if I got the general shape correct?

    The only place I think I might have went wrong is "lim y x-> -2 does not exist".

    Any help would be greatly appreciated

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  2. #2
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    Re: Please check if I drew graph correctly?

    What does "f(0), f(3) = 0, f''(1) 0" mean?

    Since f'(x) < 0 for x < -2 and -2 < x < 0, the function is monotonic on those intervals and therefore has limits from the left and from the right at -2. Since there is no overall limit, the one-sided limits must be different.

    Also, you need to make sure the function is concave/convex on the required intervals.
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  3. #3
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    Re: Please check if I drew graph correctly?

    I appreciate the quick response; maybe you're Russian, if so, огромное спасибо)

    Quote Originally Posted by emakarov View Post
    What does "f(0), f(3) = 0 mean
    I believe it means that either a local maximum or local minumum occurs at one of those points?

    Quote Originally Posted by emakarov View Post
    f''(1) 0" mean?
    I believe it means that the point of inflexion is 1.

    Quote Originally Posted by emakarov View Post
    Since f'(x) < 0 for x < -2 and -2 < x < 0, the function is monotonic on those intervals and therefore has limits from the left and from the right at -2. Since there is no overall limit, the one-sided limits must be different.
    This is the part I don't get well. The function is monotonic, but not continous, thus the shape must be the same with a small disconnect, no?

    Quote Originally Posted by emakarov View Post
    Also, you need to make sure the function is concave/convex on the required intervals.
    I also wasn't sure about this. It says "intervals", as such, does that mean it can simply "begin" being concave or convex or does it have to be completely concave/convex in those intervals? What do you think?
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  4. #4
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    Re: Please check if I drew graph correctly?

    Quote Originally Posted by Goll View Post
    I appreciate the quick response; maybe you're Russian, if so, огромное спасибо)
    Пожалуйста.

    Quote Originally Posted by emakarov View Post
    What does "f(0), f(3) = 0 mean
    Quote Originally Posted by Goll View Post
    I believe it means that either a local maximum or local minumum occurs at one of those points?
    In this case it should say "f '(0) = f '(3) = 0".

    Quote Originally Posted by emakarov View Post
    f''(1) 0" mean?
    Quote Originally Posted by Goll View Post
    I believe it means that the point of inflexion is 1.
    In this case it should say "f ''(1) = 0".

    Quote Originally Posted by Goll View Post
    This is the part I don't get well. The function is monotonic, but not continous, thus the shape must be the same with a small disconnect, no?
    Yes, though the phrase "the shape must be the same with a small disconnect" is not precise. See Wikipedia.

    Quote Originally Posted by Goll View Post
    I also wasn't sure about this. It says "intervals", as such, does that mean it can simply "begin" being concave or convex or does it have to be completely concave/convex in those intervals?
    You just need to make sure that the second derivative is as required. In your picture, (I understand that it's a sketch), the graph seems to be composed of straight lines whose second derivative is zero.
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