Consider the function, f(x) = x^3 − x^2 − 9x + 9. Answer the following: (a) State the exact roots of f(x). (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) Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it is converging to? (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 X0 = 0 and any fixed point function g(x) from part(b) that converges to the root(s).

Consider the function, f(x) = x^3 − x^2 − 9x + 9. Answer the following: (a) State the exact roots of f(x). (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) Find the convergence rate/ratio for g(x) constructed in previous part and also find which root it is converging to? (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 X0 = 0 and any fixed point function g(x) from part(b) that converges to the root(s).

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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