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Find all points on the graph of the function
f(x) = 2 cos x + cos^2 x
at which the tangent line is horizontal. (Use n as your arbitrary integer.)

smaller y-value (x,y)=

larger y-value (x,y)=

  • Calculus -

    Since the derivative is the slope of the tangent line, we need

    -2sinx - 2cosx*sinx = 0
    -2sinx(1+cosx) = 0

    sinx = 0 means x = nπ
    cosx = -1 means x = (2n+1)π

    so, f(x) has a horizontal tangent at x=nπ

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