Students were asked to evaluate f'(4) from the following table which shows values of the function f : 1 2 4 6 f(x) 4.2 4.1 4.2 4.5 5.0 5.7 • Student A estimated the derivative as f'(4) × ©)-/ (4) – 0.5, 5-4 Student B estimated the derivative as f'(4)=(4)-J(9) _03. 4-3 • Sudent C suggested that they should split the difference and estimate the average of these two results, that is fS (4)=-(05+0.3)=0.4. (a) Sketch the graph of ƒ, and indicate how the three estimates are represented on the graph. (b) Explain which answer is likely to be the best. (c) Use Student C method to find an algebraic formula to approximate f(x) using increments of size h.
Students were asked to evaluate f'(4) from the following table which shows values of the function f : 1 2 4 6 f(x) 4.2 4.1 4.2 4.5 5.0 5.7 • Student A estimated the derivative as f'(4) × ©)-/ (4) – 0.5, 5-4 Student B estimated the derivative as f'(4)=(4)-J(9) _03. 4-3 • Sudent C suggested that they should split the difference and estimate the average of these two results, that is fS (4)=-(05+0.3)=0.4. (a) Sketch the graph of ƒ, and indicate how the three estimates are represented on the graph. (b) Explain which answer is likely to be the best. (c) Use Student C method to find an algebraic formula to approximate f(x) using increments of size h.
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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Transcribed Image Text:1.
Students were asked to evaluate f'(4) from the following table which shows values of
the function f :
1
2
3
4
5
6
f(x)
4.2
4.1
4.2
4.5
5.0
5.7
Student A estimated the derivative as f'(4) =7)-J (4)_=05.
5-4
Student B estimated the derivative as f'(4)s/(4)-J (3)
4-3
= 0.3,
• Student C suggested that they should split the difference and estimate the average
of these two results, that is f'(4) (0.5+0.3) = 0.4.
(a)
Sketch the graph of f, and indicate how the three estimates are represented on
the graph.
(b)
Explain which answer is likely to be the best.
(c)
Use Student C method to find an algebraic formula to approximate f(x) using
increments of size h.
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