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(b) Given a function: (i) f(x)= x³ - 2x² - 4x + 2 Sketch the graph of f(x) in the range of x ≥ 0. (Equation Q1.2) (ii) It is known that f(x) contains two distinct roots for x ≥ 0. Compute the roots of f(x) for x 20 using Newton Raphson iteration method, taking an initial guess of x = 0 and x = 4, respectively, with a stopping criterion below 5%. (iii) Explain why the Newton Raphson iteration based on initial guess x = 2 could not yield a converged solution.

(b) Given a function: (i) f(x)= x³ - 2x² - 4x + 2 Sketch the graph of f(x) in the range of x ≥ 0. (Equation Q1.2) (ii) It is known that f(x) contains two distinct roots for x ≥ 0. Compute the roots of f(x) for x 20 using Newton Raphson iteration method, taking an initial guess of x = 0 and x = 4, respectively, with a stopping criterion below 5%. (iii) Explain why the Newton Raphson iteration based on initial guess x = 2 could not yield a converged solution.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(b) Given a function: (i) f(x) = x³ 2x² - 4x + 2 Sketch the graph of f(x) in the range of x ≥ 0. - (Equation Q1.2) (ii) It is known that f(x) contains two distinct roots for x ≥ 0. Compute the roots of f(x) for x 20 using Newton Raphson iteration method, taking an initial guess of x = 0 and x = 4, respectively, with a stopping criterion below 5%. (iii) Explain why the Newton Raphson iteration based on initial guess x = 2 could not yield a converged solution.
Transcribed Image Text:(b) Given a function: (i) f(x) = x³ 2x² - 4x + 2 Sketch the graph of f(x) in the range of x ≥ 0. - (Equation Q1.2) (ii) It is known that f(x) contains two distinct roots for x ≥ 0. Compute the roots of f(x) for x 20 using Newton Raphson iteration method, taking an initial guess of x = 0 and x = 4, respectively, with a stopping criterion below 5%. (iii) Explain why the Newton Raphson iteration based on initial guess x = 2 could not yield a converged solution.
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