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Math Help - Find critical numbers for a trig function

  1. #1
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    Find critical numbers for a trig function

    Find any critical numbers for f(x) = 2sec(x) + tan(x), 10 pi < x < 12 pi.

    When I derived it I got: f'(x) = 2(sec(x))(tan(x)) + sec2(x)
    I simplified it to: f'(x) = sec(x)(2tan(x) + sec(x))

    I need help with what to do after this step.
    Thank you for your help in advance!
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  2. #2
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    Re: Find critical numbers for a trig function

    get f' in terms of sine and cosine ...

    f'(x) = \frac{2\sin{x}+1}{\cos^2{x}} = 0

    \sin{x} = -\frac{1}{2}
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  3. #3
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    Re: Find critical numbers for a trig function

    Ok so x would be 7pi/6 and 11pi/6.

    I tried plugging it into the original equation but I didn't get my answer choices which are:
    63pi / 6
    71pi / 6
    67pi / 6
    73pi/ 6
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  4. #4
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    Re: Find critical numbers for a trig function

    Quote Originally Posted by Periwinkle38 View Post
    Ok so x would be 7pi/6 and 11pi/6.

    I tried plugging it into the original equation but I didn't get my answer choices which are:
    63pi / 6
    71pi / 6
    67pi / 6
    73pi/ 6
    did you pay attention to the domain restriction?

    Find any critical numbers for f(x) = 2sec(x) + tan(x), 10 pi < x < 12 pi.
    \color{red}\frac{60\pi}{6} < x < \frac{72\pi}{6}

    so, what are the angles in the given interval co-terminal with \frac{7\pi}{6} or \frac{11\pi}{6} ?
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