Calculus

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Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line for y=(3^1/2)x+2cos(x), 0¡Üx<2¦Ð

  • Calculus -

    For a horizontal tangent dy/dx = 0
    dy/dx = √3 - 2sinx = 0
    2sinx = √3
    sinx = √3/2

    x = 60° or 120°
    x = π/3 or 2π/3

    when x=π/3
    y = √3(π/3) + 2cos(π/3) = √3(π/3) + 2(1/2) = (π√3 + 3)/3

    when x = 2π/3
    y = √3(2π/3) + 2(-1/2) = 2√3 π - 3)/3

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