Taylor's theorem (a) Re-write this formula using step size h/2 instead of h.(b) Multiply your answer from (a) by 4, subtract (*) from the result, andthen divide everything by 3. We now should have an approximation to ƒ'(xo)based on f(xo+h, f(x− h), ƒ(xo+h/2) and ƒ(xo – h/2). What is the errorin this new approximation f'(xo)?- [7] [Richardson extrapolation for a 2nd order accurate approximation]Using Taylor's theorem, it can be shown that if ƒ € C5 ([a, b]), then thecentered difference approximation formula for the first derivative is given byf'(xo)true value=f(xo+h)-f(xo - h)2happroximationh²6h4120 (5) (5)-f"" (xo) +error(*)

First order derivative for four points.

(a) Re-write this formula using step size h/2 instead of h. (b) Multiply your answer from (a) by 4, subtract (*) from the result, and then divide everything by 3. We now should have an approximation to ƒ'(x) based on f(xo+h, f(x−h), f(xo+h/2) and f(xo-h/2). What is the error in this new approximation f'(xo)?

(a) Re-write this formula using step size h/2 instead of h. (b) Multiply your answer from (a) by 4, subtract (*) from the result, and then divide everything by 3. We now should have an approximation to ƒ'(x) based on f(xo+h, f(x−h), f(xo+h/2) and f(xo-h/2). What is the error in this new approximation f'(xo)?

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter8: Graphing Quadratic Functions

Section: Chapter Questions

Problem 17CT

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