Finding error of Newton's method

Question

So we have the following question given for homework. For the first part, I got that this would not converge quadratically because f(2)=0 and f'(2)=0. Is that correct?

For the second bit, I used ei= |r-guess at i| and substituted that for e(i+1) and ei. I simplified this to $ 1+ f(xi)/[(2-xi)*f'(xi)]$ as i goes to infinity.

What do I do from here.

Answer 1

Here is the answer I found after searching for a whole