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Math Help - For what values of x does the graph of f have a horizontal tangent?

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    For what values of x does the graph of f have a horizontal tangent?

    I cannot understand...



    F(x)=x-2sinx

    I did..f'(x)=1-2cosx=0
    cosx=1/2

    And I stop there.
    ?
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  2. #2
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    Re: For what values of x does the graph of f have a horizontal tangent?

    Quote Originally Posted by TeresaFurst28 View Post
    I cannot understand...



    F(x)=x-2sinx

    I did..f'(x)=1-2cosx=0
    cosx=1/2

    And I stop there.
    ?
    f(x) = x-2sin(x) => f'(x) = 1-2cos(x)

    Horizontal tangent when f'(x) = 0, hence we have
    1-2cos(x) = 0 <=> cos(x) = 1/2

    Now we want to find for which values of x does cos(x) = 1/2. Sketch a triangle were the hypotenuse have the length 2, the catheters (correct English?) have the length 1 and sqrt(3). The angles are then going to be pi/2 = 90, pi/3 = 60 or pi/6 = 30. By using the relationship you find that the value for x is pi/3. Therefore x = pi/3 (or x = 60) is one solution, but this is not all of the solutions.

    Since cos(x) is periodic by 2*pi (360) we have a solution for every x = pi/3+2pi*n were n is any integer. You should also know that cos(x) = cos(-x) therefore x = -pi/3+2pi*n is also a valid solution.
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  3. #3
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    Re: For what values of x does the graph of f have a horizontal tangent?

    Quote Originally Posted by TeresaFurst28 View Post
    I cannot understand...



    F(x)=x-2sinx

    I did..f'(x)=1-2cosx=0
    cosx=1/2

    And I stop there.
    ?
    please post calculus questions in the calculus forum.

    also, you need to learn the unit circle ...

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