Chapter 10.1, Problem 13E

Interpretation Introduction

Interpretation:

Using Newton’s method, with the map ${\text{x}}_{n+1}{\text{ = f(x}}_n)$, where ${\text{f(x}}_{\text{n}}{\text{) = x}}_{\text{n}}\text{- }\frac{{\text{g(x}}_{\text{n}}\text{)}}{{\text{g'(x}}_{\text{n}}\text{)}}$, show that the roots of the equation $\text{g(x) = }0$ always correspond to superscalable fixed points.

Concept Introduction:

• ➢ Determine the derivative for ${\text{f(x}}_{\text{n}}\text{)}$.

• ➢ Determine the stability from the multiplier factor.