Answered: f'(0) x 0.251255 using h = 0.1 f'(0) x…

f'(0) x 0.251255 using h = 0.1 f'(0) x 0.250313 using h = 0.05 Applying Richardson's extrapolation on the above values, we get a better approximation of f'(0) which is:

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

SectionP.6: Analyzing Graphs Of Functions

Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

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Question

I need solution (Numarical math)

Let f(x)
Using the centered 3-point formula for 1st derivatives:
(x-2)2
f'(0) x 0.251255 using h = 0.1
f'(0) x 0.250313 using h = 0.05
Applying Richardson's extrapolation on the above values, we get a better approximation of
f'(0) which is:
-0.499998
0.249999
0.234256
-1.99985

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