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Math Help - Critical numbers of Trig functions

  1. #1
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    Critical numbers of Trig functions

    Find the critical numbers on 0 < x < 2

    f(x) = 4x - 4tan(x)
    f'(x) = 4 - sec^2(x)

    f'(x) is undefined at \frac{\pi}{2} and \pi + \frac{\pi}{2}

    I figured the next answer was \frac{\pi}{3} and \pi + \frac{\pi}{3} because that makes the derivative 0, but n\pi + \frac{\pi}{3} isn't in the domain of the original function.

    So how would I go about finding the 0's?
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  2. #2
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    Quote Originally Posted by Open that Hampster! View Post
    Find the critical numbers on 0 < x < 2

    f(x) = 4x - 4tan(x)
    f'(x) = 4 - sec^2(x)

    correction ... \textcolor{red}{f'(x) = 4 - 4\sec^2{x}}
    yes, the original function and, therefore, its derivative are undefined at x = \frac{\pi}{2}

    4(1-\sec^2{x}) = 0

    \sec^2{x} = \pm 1

    only solution in the interval [0,2] is x = 0
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    Ugh, I was messing the the math tags and it must have disappeared.

    The upper bound is 2 pi, not 2.
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    Quote Originally Posted by Open that Hampster! View Post
    Ugh, I was messing the the math tags and it must have disappeared.

    The upper bound is 2 pi, not 2.
    ok, then ...

    the original function and its derivative are undefined at x = \frac{\pi}{2} and x = \frac{3\pi}{2}

    \sec^2{x} = \pm 1 at x = 0 , x = \pi , and x = 2\pi
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