Let f be a sufficiently smooth function on [2, 3] (say, f ∈ C^5 [2, 3]). Suppose that some values for f are given by the table x f(x) 2.1 2.43 2.3 2.81 2.5 3.25 2.7 3.53 2.9 3.84 Use the most appropriate forward-difference, backward-difference, three-point, fivepoint formulas to find approximations for f' (2.5). Also, use the table and an appropriate formula to find an approximation for f''(2.5).
Let f be a sufficiently smooth function on [2, 3] (say, f ∈ C^5 [2, 3]). Suppose that some values for f are given by the table x f(x) 2.1 2.43 2.3 2.81 2.5 3.25 2.7 3.53 2.9 3.84 Use the most appropriate forward-difference, backward-difference, three-point, fivepoint formulas to find approximations for f' (2.5). Also, use the table and an appropriate formula to find an approximation for f''(2.5).
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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Let f be a sufficiently smooth function on [2, 3] (say, f ∈ C^5 [2, 3]). Suppose that some values for f are given by the table
x f(x)
2.1 2.43
2.3 2.81
2.5 3.25
2.7 3.53
2.9 3.84
Use the most appropriate forward-difference, backward-difference, three-point, fivepoint formulas to find approximations for f' (2.5). Also, use the table and an appropriate formula to find an approximation for f''(2.5).
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