Hey guys, I can't get his question dealing with orders of convergence at all so any help would be nice.

Q: Find the conditions on A so that the iteration $\displaystyle x_{n+1}=x_n-Af(x_n)$ will converge to a root of f if stared near the root.

I know I should look at the taylor series expansion of f about its root but I am stuck with working out.

Thanks for your help!