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26 May, 20:36

For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable. Enter your answers as a comma-separated list.)

f (x) = x - 2 sin x

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  1. 26 May, 20:47
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    F (x) = x - 2sinx

    To find for what values of x graph has tangents we need to differentiate function f (x).

    f' (x) = 1-2cosx

    Now, if we want to have horizontal tangents we need to make function f' (x) equal to 0 because at minimum or maximum of function f (x) tangent is horizontal.

    1-2cosx = 0

    cosx = 1/2

    x = pi/3 + 2*n*pi and

    x = - pi/3 + 2*n*pi

    Explanation: cosx = 1/2 for both 60° and - 60°. If we make one circle cosx will be equal to 1/2 for 420 and 300 degrees. Writing degrees in radians (using pi) we can write formulas above where 2*pi represents one full circle and n is an integer which represents how many circles we made.
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