Counterexample

Is this true?

Newton's method always converges from any starting point

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Numerical convergence

A scheme assumed to converge, or to converge at its advertised rate.

Drill statements like this

Go deeper· Explained in full in Root finding and orders of convergence· Asked in CSIR NET December 2025· From Numerical Analysis › Root finding: bisection, Newton–Raphson, fixed point, order of convergence

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