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Consider the polynomial f (x) = 3-5x - x3. Using the forward-divided difference

Consider the polynomial f (x) = 3-5x - x3. Using the forward-divided difference

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the polynomial f (x) = 3-5x – x3. %3D Using the forward-divided difference approximation for the first derivative with step size h = 2, we obtain f' (2.4) z - 40.68. Divide the step size in half successively until you get a step size small enough to have an approximation of f' (x) correct to at least two significant figures. That is, you have to approximate f'(2.4) with h = 1,0.5,0.25,. %3D You cannot use the exact value of f' (2.4) to determine the answer. The step sizeh = %3D it is enough to have at least two correct significant figures in the approximation of f(x). The corresponding approximation is f'(2.4) - and the approximate percent relative absolute error is | ɛa | = %.
Transcribed Image Text:Consider the polynomial f (x) = 3-5x – x3. %3D Using the forward-divided difference approximation for the first derivative with step size h = 2, we obtain f' (2.4) z - 40.68. Divide the step size in half successively until you get a step size small enough to have an approximation of f' (x) correct to at least two significant figures. That is, you have to approximate f'(2.4) with h = 1,0.5,0.25,. %3D You cannot use the exact value of f' (2.4) to determine the answer. The step sizeh = %3D it is enough to have at least two correct significant figures in the approximation of f(x). The corresponding approximation is f'(2.4) - and the approximate percent relative absolute error is | ɛa | = %.
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