calculus

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For what values of x does the graph of f(x)=x+2sinx have a horizontal tangent?

  • calculus -

    f'(x) = 1 + 2cosx
    = 0 for a horizontal tangent , (slope=0)

    2cosx = -1
    cosx = -1/2

    x must be in quadrants II or III
    and I know that cos π/3 = +1/2

    x = π-π/3 or x = π + π/3
    x = 2π/3 or x = 4π/3 , for 0 ≤ x ≤ 2π

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