Practice question · True or false
Newton's method is always preferable to bisection because it converges quadratically.
Hints
- What does Newton need that bisection does not?
- Bisection cannot fail once it has a sign change.
Show the answer
False
Why
False. Newton needs a derivative and a good starting guess, and it can diverge, cycle, or divide by a near-zero derivative. Bisection is slow and guaranteed once it brackets a sign change. Robust solvers combine them, Brent's method, taking Newton steps when they behave and bisecting when they do not.
Practise Root Finding
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