LaTeX
x_{n+1}=x_n-\frac{f(x_n)}{f\prime(x_n)}Variables
- Define every symbol and unit before substitution.
- Check the domain, shape, and convention required by the formula.
How to use this formula
Iteratively approximates a root of a differentiable function.
Important notes
- Verify assumptions and units before applying the expression.
- Keep exact values until the final rounding step when possible.
Quick example
Use the newton method iteration with a small known example, then verify the result independently.
Applicability, worked calculation, and verification
Assumptions and domain checks
- For the Newton Method Iteration, verify assumptions and units before applying the expression.
- For the Newton Method Iteration, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- The iteration, step size, tolerance, and stopping rule must be suitable for the problem and the method must converge in the chosen region.
Worked example
Use the newton method iteration with a small known example, then verify the result independently.
Common mistakes
- When copying Newton Method Iteration, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Do not report a numerical approximation without a tolerance, convergence check, and an estimate of rounding or truncation error.
Continue the workflow
Use Newton Method Iteration in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
x_{n+1}=x_n-\frac{f(x_n)}{f\prime(x_n)}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Newton Method Iteration used for?
Iteratively approximates a root of a differentiable function.
Can I copy this formula as LaTeX?
Yes. Copy x_{n+1}=x_n-\frac{f(x_n)}{f\prime(x_n)} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.