Explanation Method used: Newton’s Method: 1. Pick an initial estimate x 0 of the root c. 2. Find a new estimate using the iterative formula x n + 1 = x n − f ( x n ) f ′ ( x n ) , n = 0 , 1 , 2 , … 3. Compute | x n − x n + 1 | . If the number is less than a prescribed positive number, then stop the iteration. The required approximation to the root x = c is x = x n + 1 . Calculation: The function is given by f ( x ) = − x 3 − 2 x + 2 . Find the derivative of f ( x ) = − x 3 − 2 x + 2 as follows. f ′ ( x ) = − 3 x 2 − 2 The required iterative formula is, x n + 1 = x n − − x n 3 − 2 x n + 2 − 3 x n 2 − 2 = − 3 x n 3 − 2 x n + x n 3 + 2 x n − 2 − 3 x n 2 − 2 = − ( 2 x n 3 + 2 ) − ( 3 x n 2 + 2 ) = 2 x n 3 + 2 3 x n 2 + 2 By using the above mentioned Newton’s method, find x 1 at x 0 = 1

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 11.7, Problem 7E

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To find: The zero of a function f(x)=−x3−2x+2 if an initial estimation is x0=1 and approximate the answer to four decimal places.

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Chapter 11.7, Problem 6E

Chapter 11.7, Problem 8E

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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The zero of a function f ( x ) = − x 3 − 2 x + 2 if an initial estimation is x 0 = 1 and approximate the answer to four decimal places.

Solution Summary: The author explains Newton's method of finding the zero of a function f(x)=-x

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To find: The zero of a function f(x)=−x3−2x+2 if an initial estimation is x0=1 and approximate the answer to four decimal places.

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Chapter 11 Solutions