Need a please 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.

Note: As per your requirement, I answered here only part (a). Consider a function f(x) =…

Answered: Consider A function f(x)= x³ - 7x² + 4x…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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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. Consider the function g(x) = 5 - 6/x a- Show that the function g(x) has a fixed point in the interval [2.5,3.5]. b- Find a root using Fixed Point Iteration. Use po = 2.6, to calculate the relative error.
Suppose that the weekly sales S of a product are given by er Sup 20t S(t) = thousand dollars, t2 + 25 where t is the number of weeks since sales began. Suppose that the product has only been on sale for 15 weeks, so 0 < t< 15. Over what time interval are sales increasing? Enter your answer using interval notation, for example, something like [2, 8). What are the maximum weekly sales during this period? thousand dollars.
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Consider A function f(x)= x³ - 7x² + 4x + 12. Construct two different fixed point functions g(x) such that f(x) = 0. (a)