Let f (x) =(x+1)3Using the centered 3-point formula for 1* derivatives:%3Df'(0) -0.502509 using h = 0.1%3Df'(0) x -0.500626 using h = 0.05%3DApplying Richardson's extrapolation on the above values, we get a better approximation off'(0) which is:O 0.249999O 0.234256O -1.99985-0.499998

Solution Using Richardson's Extrapolation:

Let f (x) = (x+1)3 Using the centered 3-point formula for 1* derivatives: %3D f'(0) -0.502509 using h = 0.1 %3D f'(0) -0.500626 using h = 0.05 Applying Richardson's extrapolation on the above values, we get a better approximation of f'(0) which is:

Let f (x) = (x+1)3 Using the centered 3-point formula for 1* derivatives: %3D f'(0) -0.502509 using h = 0.1 %3D f'(0) -0.500626 using h = 0.05 Applying Richardson's extrapolation on the above values, we get a better approximation of f'(0) which is:

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

Let f (x) =
(x+1)3
Using the centered 3-point formula for 1* derivatives:
%3D
f'(0) -0.502509 using h = 0.1
%3D
f'(0) x -0.500626 using h = 0.05
%3D
Applying Richardson's extrapolation on the above values, we get a better approximation of
f'(0) which is:
O 0.249999
O 0.234256
O -1.99985
-0.499998

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