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Math Help - Analyze trig function

  1. #1
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    Analyze trig function

    I'd like to verify if this is right..

    y=2cos(x)+sin(2x)
    y ' = 2(-sin(x)+cos(2x))
    y '' = -2(cos(x)+2sin(2x))

    So I can use the y' to get the maximum, since pi/6 will give zero for the inside there. How can I analyze the y''? Change the 2sin(2x) to 4sinxcosx? I tried that and so then you can take out the cosx, which would mean that pi/2 would be one of the zeroes. What about the inside? (1+4sinx)?
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  2. #2
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    Quote Originally Posted by theowne View Post
    I'd like to verify if this is right..

    y=2cos(x)+sin(2x)
    y ' = 2(-sin(x)+cos(2x))
    y '' = -2(cos(x)+2sin(2x))

    So I can use the y' to get the maximum, since pi/6 will give zero for the inside there. How can I analyze the y''? Change the 2sin(2x) to 4sinxcosx? I tried that and so then you can take out the cosx, which would mean that pi/2 would be one of the zeroes. What about the inside? (1+4sinx)?
    looks good so far

    1+4\sin(x)=0 \iff \sin(x)=-\frac{1}{4} \iff x=\sin^{-1}\left(\frac{-1}{4} \right)
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  3. #3
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    So if the domain specifies between 0 and pi, do you discard that answer?
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