A fixed point is unstable if nearby points move
away from the fixed point under graphical iteration. |
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Click the picture for an animation. |
A fixed point is unstable if at the fixed point the tangent line to the graph
lies outside the region between +45° and -45°. |
That is, its slope is greater than +1 or less than -1. |
The region between these lines is shaded in blue.
If the graph crosses the diagonal outside the
blue region (on both sides), the fixed point is unstable. |
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