Need a,b 1. Consider A function f(x) = x³ - 7x² + 4x + 12.(a)(b)(c)(d)(e)Construct two different fixed point functions g(x) such that f(x) = 0.Compute the convergence rate of each fixed point function g(x) obtained in the previous part, andstate which root it is converging to or diverging.How many iterations will be required to find the root if the machine epsilon is 1.4 x 10-18.Show 4 iterations using the Bisection Method to find the root of the above function within theinterval [4.25, 8.95].Starting from xo = 2.26 find the approximate root of f(x) up to four iterations by applying Aitkenacceleration appropriately. Express your result up to five decimal places.

Answered: 1. Consider A function f(x) = x³ - 7x²…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 1CR

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4. Consider the function, f(x) = x³ = x² - 9x +9. Answer the following: State the exact roots of f(x). (a) (b) Construct three different fixed point functions g(x) such that f(x) = 0. (Make sure that one of the g(x)'s that you constructed converges to at least a root). (c) (d) Find the approximate root, x, of the above function using fixed point iterations up to 4 significant figures within the error bound of 1 × 10-³ using xo = 0 and any fixed point function g(x) from part(b) that converges to the root(s). Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it is converging to?
2. Determine the highest real root of f(x) = 2x³ - 11.7x² +17.7x-5 a. Graphically b. Fixed-point iteration method (three iterations, xo =3). Note: Make certain that you develop a solution that converges on the root.
3. Consider the equation f(x) = x³ - 2x² – 11x + 12 on the interval [1.78, 8.25]. (a) Find the minimum number of iterations required to find the root of the given equation within the error bound of 1 x 10-3. (b) Show 5 iterations using the Bisection Method to find the root of the above function within the interval [1.78, 8.25].
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1. Consider A function f(x) = x³ - 7x² + 4x + 12. (a) (b) Construct two different fixed point functions g(x) such that f(x) = 0. 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.