Parallel Tangents To A Curve

Calculus Level 3

The following is the plot of \(f(x)=x+\cos x\). Points \(A\), \(B\), \(C\) and \(D\) have abscissae \(2\), \(\pi\), \(2\pi\) and \(8\), respectively. The line tangent to the graph at one of these points is parallel to the tangent at another point. Determine the pair(s) that satisfy(ies) this property.

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