# 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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