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Math Help - Find x values of stationary points

  1. #1
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    Wink Find x values of stationary points

    Find the values of x at the stationary points for sin(x^2)

    I found the 1st derivative which is 2xcos(x^2)

    I know the final answer is x = 0 and x = \pm sqrt((k+(1/2))pi) for k = 0,1,2....

    How do you get that answer?? I can see how the answer is x = 0, but how do you figure out the other one?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by brumby_3 View Post
    Find the values of x at the stationary points for sin(x^2)

    I found the 1st derivative which is 2xcos(x^2)

    I know the final answer is x = 0 and x = \pm sqrt((k+(1/2))pi) for k = 0,1,2....

    How do you get that answer?? I can see how the answer is x = 0, but how do you figure out the other one?
    When is cos(x^2)=0?
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  3. #3
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    Quote Originally Posted by alexmahone View Post
    When is cos(x^2)=0?
    for all integers?
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by brumby_3 View Post
    for all integers?
    No.

    cos(x^2)=0 when x^2=(k+(1/2))pi for k = 0,1,2....

    So, x=?
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  5. #5
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    is it sqrt[(k+(1/2))pi]
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  6. #6
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by brumby_3 View Post
    is it sqrt[(k+(1/2))pi]
    Don't forget the \pm.
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