Calculus grade 12

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find the coordinates of all points on the graph of f(x) = x + 2cos(x) in the interval [0, pie] at which the tangent line is horizontal.

  • Calculus grade 12 -

    f'(x) = 1 - 2sinx
    = 0 for a horizontal slope
    1-2sinx = 0
    sinx = 1/2
    x = π/6 or 5π/5

    if x = π/6
    y = π/6 + √3 = (π + 6√3)/6 ---> point (π/6 , (π+6√3)/6

    if x = 5π/6
    y = 5π/6 - √3 = (5π - 6√3)/6 ---> point (5π/6 , (5π-6√3)/6 )

  • Calculus grade 12 -

    thank you reiny

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