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Math Help - Derivative to Find Horizontal Tangent

  1. #1
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    Derivative to Find Horizontal Tangent

    f(x)= 2secx + tanx for all x in the interval 0 and 2pi

    Am i supposed to take the derivative of f(x), set it equal to 0, and find all points where x satisfies the equation?
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  2. #2
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    Quote Originally Posted by NotEinstein View Post
    f(x)= 2secx + tanx for all x in the interval 0 and 2pi

    Am i supposed to take the derivative of f(x), set it equal to 0, and find all points where x satisfies the equation?
    Oh yeah
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  3. #3
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    I'm breaking this problem down, and am stuck at

    2(sinx/cos^2(x))+1+tan^2(x)

    did I mess up the process somewhere, or am i just needing to go further?
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  4. #4
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    f'(x) =2 \sec{x} \tan{x} + \sec^2{x}
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    Quote Originally Posted by 11rdc11 View Post
    f'(x) =2 \sec{x} \tan{x} + \sec^2{x}
    i got that, but i need to plug in to find points where there is a horizontal tangent.. so now I am trying to simplify this derivative.
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  6. #6
    Super Member 11rdc11's Avatar
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    Factor out a \sec{x}

    \sec{x}(2\tan{x} + \sec{x})= 0


    so now you have

    \sec{x} = 0 and 2\tan{x} + \sec{x} =0 and you don't have to worry about sec(x) = 0 since that is not possible





    \frac{2\sin{x}}{\cos{x}}+ \frac{1}{\cos{x}} = 0

    \frac{2\sin{x} + 1}{\cos{x}}

    2\sin{x} + 1 = 0

    2\sin{x} = -1

    \sin{x} = -\frac{1}{2}

    x= \frac{7\pi}{6} and  x= \frac{11\pi}{6}
    Last edited by 11rdc11; September 17th 2008 at 04:16 PM. Reason: Correction forgot the other solution
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  7. #7
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    Quote Originally Posted by 11rdc11 View Post
    Factor out a \sec{x}

    \sec{x}(2\tan{x} + \sec{x})= 0


    so now you have

    \sec{x} = 0 and 2\tan{x} + \sec{x} =0 and you don't have to worry about sec(x) = 0 since that is not possible





    \frac{2\sin{x}}{\cos{x}}+ \frac{1}{\cos{x}} = 0

    \frac{2\sin{x} + 1}{\cos{x}}

    2\sin{x} + 1 = 0

    2\sin{x} = -1

    \sin{x} = -\frac{1}{2}

    x= \frac{7\pi}{6}
    i followed it all the way til the end. how did you figure that x = 7pi/6?
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