Question *A formula of order 4 for approximating the first derivative of a function f gives:f'(0) z 4.50557 for h = 1f'(0) 2.09702 for h 0.5By using Richardson's extrapolation on the above values, a better approximationof f'(0) is:

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Answered: Question A formula of order 4 for…

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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Given to the right is the graph of f'(x), the DERIVATIVE of a function f(x). Use this graph to answer the following questions, estimating as accurately as possible from the graph. (a) On what interval(s) is f(x) decreasing? Briefly explain how you chose your interval(s). (b) On what interval(s) is f(x) concave up? Briefly explain how you chose your interval(s). (c) List all places where f(x) has a local minimum value. Briefly explain how you chose your answer(s). (d) List all places where f'(x) has a local minimum value.
Let the following function: f(x) %3 3 х2— 10 х3 + 5х4 1. Express the derivative of f:f' (x). 2. Calculate the exact value off'(0.2). 3. By taking h=0.001 as a step size and working to 4 decimal places throughout. a) Use forward difference (FD) method to estimate f'(0.2). Calculate the corresponding error (EFD) b) Use backward difference (BD) method to estimate f'(0.2). Calculate the corresponding error (EBD) c) Use central difference (CD) method to estimate f'(0.2). Calculate the corresponding error (EcD)
Take h = 0.1. Use three-point centered-difference formula to approximate the first derivative of f(x)=a at x = 3. Round your answer to 3 decimal places.
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Question A formula of order 4 for approximating the first derivative of a function f gives: f'(0) - 4.50557 for h = 1 f'(0) × 2.09702 for h = 0.5 By using Richardson's extrapolation on the above values, a better approximation of f'(0) is: