Explanation Given: The function is f ( x ) = x 2 − 6 , x 0 = 2 . Formula used: Newton method: x n + 1 = x n − f ( x n ) f ′ ( x n ) Calculation: The function is f ( x ) = x 2 − 6 , x 0 = 2 . We have to find the value of x 1 , x 2 and x 3 . Find the derivative of function. f ′ ( x ) = 2 x Use the formula: x n + 1 = x n − f ( x n ) f ′ ( x n ) Compute the successive approximations. First, find the value of x 1 . x 1 = x 0 − f ( x 0 ) f ′ ( x 0 ) = x 0 − x 0 2 − 6 2 x 0 Substitute 2 for x 0 in the above function. x 1 = 2 − ( 2 ) 2 − 6 2 ( 2 ) = 2 − 4 − 6 4 = 2 + 2 4 = 2.5 Now, find the value of x 2 . x 2 = x 1 − f ( x 1 ) f ′ ( x 1 ) = x 1 − x 1 2 − 6 2 x 1 Substitute 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.7, Problem 1E

To determine

Use Newton method to f and initial guess x0 to find x1,x2 and x3.

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Chapter 4 Solutions

Calculus - Standalone book

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Use Newton method to f and initial guess x 0 to find x 1 , x 2 and x 3 .

Solution Summary: The author explains Newton's method to determine the value of x_1, and the derivative of function.

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Use Newton method to f and initial guess x0 to find x1,x2 and x3.

Chapter 4 Solutions