3 1. Consider a function f(x) = x³ + x² - 4x 4. (a) Compute the minimum number of iterations required to find the root within the interval [-10, -1.5] if the machine epsilon(error bound) is 1 x 10^-2. (b) Show 5 iterations using the Bisection Method to find the root of the above function within the interval [-10, -1.5].

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 7E
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Need ans for part a and b
3
1. Consider a function f(x) = x³ + x² - 4x 4.
(a)
Compute the minimum number of iterations required to find the root within the
interval [-10, -1.5] if the machine epsilon(error bound) is 1 x 10^-2.
(b)
Show 5 iterations using the Bisection Method to find the root of the above function
within the interval [-10, -1.5].
(c)
State the exact roots of f(x) and construct two different fixed point functions g(x)
such that f(x) = 0.
(d)
Compute the convergence rate of each fixed point function g(x) obtained in the
previous part, and state which root it is converging to or diverging.
Transcribed Image Text:3 1. Consider a function f(x) = x³ + x² - 4x 4. (a) Compute the minimum number of iterations required to find the root within the interval [-10, -1.5] if the machine epsilon(error bound) is 1 x 10^-2. (b) Show 5 iterations using the Bisection Method to find the root of the above function within the interval [-10, -1.5]. (c) State the exact roots of f(x) and construct two different fixed point functions g(x) such that f(x) = 0. (d) Compute the convergence rate of each fixed point function g(x) obtained in the previous part, and state which root it is converging to or diverging.
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