Newton-Raphson Method
This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.
- Newton-Raphson Method
A method that is often used in computers for finding the zeros of a function using derivatives. Its formula is
- Related Glossary Terms
- Index
Chapter 3 - Approximation and Second Derivatives
Glossary and deeper reading · 1 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
-
Newton’s method
Newton’s method estimates a root by repeatedly replacing the current input with the horizontal intercept of its tangent line. The update is xₙ₊₁=xₙ−f(xₙ)/f′(xₙ) where the denominator is nonzero. For example, starting at 2 for f(x)=x²−2 produces the next estimate 1.5. A poor starting value or problematic derivative can cause failure, so convergence is not guaranteed.
Read more: Original source · Newton–Raphson Method (beyond AB) →