2. The function f(x) is discretized using an equidistant grid with step h. It is known that f(0) = 1, f(h) = 2 and f(2h) = 1. (a) Determine h, if the central difference approximation to the second derivative at r = h is f" (h) = -2. (b) Determine the most accurate approximation to f'(h). Give the name of the approximation.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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2.
The function f(x) is discretized using an equidistant grid with step h. It is
known that f(0) = 1, f(h) = 2 and f(2h) = 1.
(a) Determine h, if the central difference approximation to the second derivative at r = h is
f" (h) = -2.
%3D
(b) Determine the most accurate approximation to f'(h). Give the name of the approximation.
Transcribed Image Text:2. The function f(x) is discretized using an equidistant grid with step h. It is known that f(0) = 1, f(h) = 2 and f(2h) = 1. (a) Determine h, if the central difference approximation to the second derivative at r = h is f" (h) = -2. %3D (b) Determine the most accurate approximation to f'(h). Give the name of the approximation.
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