Q1. (1) The finite-divided difference approximations of the first derivative of the function f(x) can be f(x,,) – f(x,) f'(x,) = (Eqn.1) or f'(x,) = f(x,)- f(x_1) (Eqn. 2) 2h Which approximation has a better accuracy? Prove your answer through error analysis.

Q1. (1) The finite-divided difference approximations of the first derivative of the function f(x) can be f(x,,) – f(x,) f'(x,) = (Eqn.1) or f'(x,) = f(x,)- f(x_1) (Eqn. 2) 2h Which approximation has a better accuracy? Prove your answer through error analysis.

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

Topic: numerical methods Sub topic: error analysis

Q1. (1) The finite-divided difference approximations of the first derivative of the function f(x) can be
f'(x,) = *)- f(x,)
h
(Eqn. 1)
or
f'(x,) =
f(X,)- f(x,) .
(Eqn. 2)
2h
Which approximation has a better accuracy? Prove your answer through error analysis.

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