Practice question · Multiple choice
Newton's method converges fast but not from every starting point. What can go wrong?
Hints
- Draw a tangent at a point where the curve is nearly flat.
- Where does that tangent cross the axis?
Show the answer
C. The tangent can send the iterate far away or into a cycle
Why
Newton is locally fast and globally unreliable. Bisection is the reverse, slow and guaranteed, which is exactly why production root-finders combine them.
Practise Root Finding
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