Practice question · Multiple choice
Newton’s method races to a root when it works, but pick the starting point badly and it fails. Which situation breaks it?
Hints
- Each step is . Look for the danger in that fraction.
- Dividing by a near-zero slope launches the next guess toward the horizon.
Show the answer
C. Starting where
Why
A flat tangent barely tilts toward zero, so its root-crossing lies absurdly far away: division by catapults the iteration. Away from flat spots, though, the method roughly doubles the correct digits every step: flawed and brilliant at once.
Practise Graphs, approximation, and numerical sense
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