Complete tasks "i" through "iv" for parts a, b, and c. Be sure to use the specified function values. 3. Find the most accurate finite difference formula and the corresponding leading error term for thefollowing derivatives:(a) ƒ"(x)(b) f(iv) (x)(c) f(x) - 3f'(x)to the highest order of accuracy possible using only the following function values.i fi-2, fi-1, fi, fi+1, and fi+2ii fi, fi+1, fi+2, fi+3, and fi+4iii fi-4, fi-3, fi-2, fi-1, and fiiv fi-1, fi, fi+1, fi-1, fi, and fi+11

the solution is an given below :

Answered: Find the most accurate finite…

Engineering

Computer Science

Find the most accurate finite difference formula and the corresponding leadi following derivatives: (a) f"(x)

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter14: Numerical Methods

Section14.6: The Trapezoidal Rule

Problem 3E

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exponential time complexity. So there is a need to figure out a better method than this.

Question

Complete tasks "i" through "iv" for parts a, b, and c. Be sure to use the specified function values.

3. Find the most accurate finite difference formula and the corresponding leading error term for the
following derivatives:
(a) ƒ"(x)
(b) f(iv) (x)
(c) f(x) - 3f'(x)
to the highest order of accuracy possible using only the following function values.
i fi-2, fi-1, fi, fi+1, and fi+2
ii fi, fi+1, fi+2, fi+3, and fi+4
iii fi-4, fi-3, fi-2, fi-1, and fi
iv fi-1, fi, fi+1, fi-1, fi, and fi+1
1

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