The slope of the line \(y=2x\) is 2, and any parallel line will have the same slope. Since \(f'(x_0)\) gives the tangent line to \(y=f(x)\) at \(x=x_0\), any tangent line will be parallel whenever
\(\arctan(x^3-x)=2\)
But this never happens, since \(|\arctan x|\le\dfrac\pi2<2\)
So there will never be a tangent line with slope 2, and thus no tangent line parallel to \(y=2x\).
