I have come across the following exercise in Kosinski's 'Differential Manifolds':
Exercise: Consider an imbedding $\mathbb R\to \mathbb R^3$ where the image is "the line with a knot":
Show that this imbedding is isotopic to the standard imbedding $\mathbb R\subset \mathbb R^3$.
But I cannot see what such an isotopy could possibly do to unknot this knot? The only thing I can think of is pulling the knot at both ends to tie it completely tight at the origin. But then I would necessarily cause the second derivative to explode, wouldn't I? What else is there to do? Or am I possibly wrong in thinking that the pulling gives me trouble with higher derivatives?
Thanks for your help!