The curve \(C\) has equation \(y=\frac{2 x^{2}+k x}{x+1}\), where \(k\) is a constant. Find the set of values of \(k\) for which \(C\) has no stationary points.

For the case \(k=4\), find the equations of the asymptotes of \(C\) and sketch \(C\), indicating the coordinates of the points where \(C\) intersects the coordinate axes.