A fixed point is stable if nearby points iterate toward the fixed point under graphical iteration.
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| Click the picture for an animation. |
A fixed point is stable if at the fixed point the tangent line to the graph lies between +45 degrees and -45 degrees.
That is, its slope lies between +1 and -1.
The region between these lines is shaded in blue. If the graph crosses the diagonal inside the blue region (on both sides), the fixed point is stable.
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