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Math Help - extremum

  1. #1
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    extremum

    Find all extrema in the interval  [0,2{\pi}] if y=x + sin x.
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  2. #2
    Eater of Worlds
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    First, find your derivative.

    f'(x)=1+cos(x)

    1+cos(x)=0

    What solutions to this fall in your interval?.

    Here's a graph. They always help.
    Last edited by galactus; November 24th 2008 at 05:39 AM.
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  3. #3
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    is it

    a)  (-1,-1+ \frac {3\pi} {2}), (0,0)
    b) (2 {\pi}, 2{\pi}) (0,0)
    c) (2{\pi}, 2{\pi}), ({\pi},{\pi})
    d) ({\pi},{\pi}), (0,0)
    e) None of these
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  4. #4
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    Quote Originally Posted by Samantha View Post
    is it

    a)  (-1,-1+ \frac {3\pi} {2}), (0,0)
    b) (2 {\pi}, 2{\pi}) (0,0)
    c) (2{\pi}, 2{\pi}), ({\pi},{\pi})
    d) ({\pi},{\pi}), (0,0)
    e) None of these
    Have you looked at Galactus's plot? Are there any local maxima or minima?
    Where are the global maximum and minimum in [0,2 \pi ]?

    RonL
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    Have you looked at Galactus's plot? Are there any local maxima or minima?
    Where are the global maximum and minimum in [0,2 \pi ]?

    RonL
    I'mnot sure =(
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  6. #6
    Eater of Worlds
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    I'm sorry to say, you should see your professor if you're that lost.
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  7. #7
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    That's how I did it and understand it. Plz help

    y=x+sinx
    y(prime)=1+cosx
    cosx=-1
    x= \pi

    so the answer it (\pi, \pi)
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  8. #8
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    Quote Originally Posted by Samantha View Post
    That's how I did it and understand it. Plz help

    y=x+sinx
    y(prime)=1+cosx
    cosx=-1
    x= \pi

    so the answer it (\pi, \pi)
    Evidently from the graph the function only has extrema at the ends of the interval since it is monotonically increasing. So the extrema are at x = 0 and x = 2*pi.

    -Dan
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  9. #9
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    Quote Originally Posted by topsquark View Post
    Evidently from the graph the function only has extrema at the ends of the interval since it is monotonically increasing. So the extrema are at x = 0 and x = 2*pi.

    -Dan
    Then the answer is (2\pi, 2\pi), (0,0)?
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  10. #10
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Samantha View Post
    Then the answer is (2\pi, 2\pi), (0,0)?
    Looks like it. The critical points within the interval are obviously not relative max or min points (which you can tell by graphing or the second derivative test, whichever you prefer.)

    -Dan
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