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Math Help - question about graph

  1. #1
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    question about graph

    If you're given a graph of f', how can you tell where there are local min or max in f?

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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by kwivo View Post
    If you're given a graph of f', how can you tell where there are local min or max in f?

    what does it mean when f'(x)=0?
    what are the intervals where f'(x)>o and f'(x)<0?
    what does it imply when f'(x_0 + \Delta x) >0 and f'(x_0 - \Delta x)<0 or the other way around?

    maybe, i can't wait for your reply.. anyways, these are the interpretations..
    if f'(x_0) = 0, then surely, f has a rel min or max at x_0
    suppose, f'(x_0 + \Delta x) >0 and f'(x_0 - \Delta x) <0, then f assumes a rel min at x=x_0; for the other case, f assumes a relative max..
    Last edited by kalagota; November 4th 2007 at 06:40 AM.
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  3. #3
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    When f'(x)=0, that's a critical point. If f'(x)>0, then that's where f(x) is increasing; f'(x)<0, f(x) is decreasing.

    I don't get what the last one mean.


    Ok, so I got local max at x=2. Then I got min at x=4,x=8. Am I missing something for max because I didn't get the right answer.
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by kalagota View Post
    what does it mean when f'(x)=0?
    what are the intervals where f'(x)>o and f'(x)<0?
    what does it imply when f'(x_0 + \Delta x) >0 and f'(x_0 - \Delta x)<0 or the other way around?

    maybe, i can't wait for your reply.. anyways, these are the interpretations..
    if f'(x_0) = 0, then surely, f has a rel min or max at x_0
    suppose, f'(x_0 + \Delta x) >0 and f'(x_0 - \Delta x) <0, then f assumes a rel min at x=x_0; for the other case, f assumes a relative max..
    i think i should have used \delta x there..
    maybe this one, if a < x_0 < b such that f'(x_0)=0, and f'(x)<0 for all x \in (a,x_0) and f'(x)>0 for all x \in (x_0, b), then f assumes a rel min at x=x_0;
    for the other case, i.e. if f'(x)>0 for all x \in (a,x_0) and f'(x)<0 for all x \in (x_0, b), then f assumes a relative max
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  5. #5
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by kwivo View Post
    When f'(x)=0, that's a critical point. If f'(x)>0, then that's where f(x) is increasing; f'(x)<0, f(x) is decreasing.
    right..

    Quote Originally Posted by kwivo View Post
    Ok, so I got local max at x=2. Then I got min at x=4,x=8. Am I missing something for max because I didn't get the right answer.
    indeed!!
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