I am stuck at the following exercise:
For which starting points for $f(x) := \sqrt{1+x^2}$ does Newtons Method converge?
I recently learned about Newton's Method in class and the real theorem related to it that we did was that Newton's Method (under some regularity conditions) converges to a stationary point $x^*$ of $f \in \mathcal{C}^2$ if the starting point $x_0$ is sufficiently close to $x^*$.
However, I do not see how to apply this here. Could you please give me a hint?