Derive the following formula for approximating the derivative f": 1 f"(x) ≈ (-f(x+2h) + 16f (x + h) — 30f(x) + 16ƒ (x − h) − f (x − 2h)) 12h² What is the Big-Oh error term?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 4CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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Q2. Derive the following formula for approximating the derivative f":
f" (x) ~
1
(-f(x+ 2h) + 16f(x+ h) – 30f(x)+ 16ƒ(x – h) – f(x – 2h))
12h2
What is the Big-Oh error term?
Transcribed Image Text:Q2. Derive the following formula for approximating the derivative f": f" (x) ~ 1 (-f(x+ 2h) + 16f(x+ h) – 30f(x)+ 16ƒ(x – h) – f(x – 2h)) 12h2 What is the Big-Oh error term?
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,