Use Excel and start at x0 = 1, x0 = -1/5, x0 = 1/9 (make 3 different colors)Make sure you include step by step and show each equations 4 Show that Newton's method for f(x) = x3 gives thestrange formula x+1=-2x,. Draw a graph to show theiterations.

Newton's Method: xn+1 = xn-fxnf'xn…

Answered: Show that Newton's method for S(x) = x…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Use Excel and start at x0 = 1, x0 = -1/5, x0 = 1/9 (make 3 different colors)

Make sure you include step by step and show each equations

4 Show that Newton's method for f(x) = x3 gives the
strange formula x+1=-2x,. Draw a graph to show the
iterations.

Expert Solution

Step 1: Given function and plot

Newton's Method:

$x_{n + 1} = x_{n} - \frac{f (x_{n})}{f' (x_{n})} (1) G i v e n, f (x) = x^{\frac{1}{3}} (2) f' (x) = \frac{1}{3} x^{\frac{- 2}{3}} (U s e \frac{d}{d x} x^{n} = n x^{n - 1}) (3) U s e (2) & (3) i n (1) x_{n + 1} = x_{n} - \frac{{x_{n}}^{\frac{1}{3}}}{\frac{1}{3} {x_{n}}^{\frac{- 2}{3}}} x_{n + 1} = x_{n} - 3 x_{n} x_{n + 1} = - 2 x_{n} (4)$