Given the following fixed point iteration $x_{n+1}=\frac{112233+Ax_n^2}{Bx_n}$ find values for A,B s.t the iteration converges to $\alpha$ (a root) with maximal order of convergence. Find the order.
After simplifying it we get that $G(x)=\frac {112233}{Bx}+\frac A Bx$. We want to find $K>0$ bounds the derivative. $G\prime(x)=-\frac{112233}{Bx^2}+\frac A B$ but I can't bound it since in [0,1] (No interval was mentioned so maybe the writer meant convergence on $(-\infty,\infty)$) the derivative is not bounded. What conditions can I require on A,B s.t the iteration converges?
HINT:the max order means the highest derivative that is different from 0.