Key in the function [math]f\left(x\right)[/math] and the initial value [math]x_0[/math], then move the slider to see the first few values of the recurrence relation [math]x_{n+1}=f\left(x_n\right)[/math]. Under appropriate conditions, the sequence [math]\left\{x_n\right\}[/math] will converge to a root of the equation [math]x=f\left(x\right)[/math].[br][br]What are these appropriate conditions? Why does it converge to some roots and not others?