Explanation Given: The given equation is f ( x ) = x 3 − 3 x + 6 Initial approximation = x 1 = 1 Calculation: When the curve is sketched and the tangent is drawn at x 1 = 1 , it can be seen that the tangent line is parallel to the x-axis. Therefore, the Newton’s method fails. The given function does not intersect the x-axis anywhere, therefore, it has no real root, and therefore the approximation x 1 = 1 is meaningless. Hence, the Newton’s method fails. Since, f ( x ) = x 3 − 3 x + 6 f ' ( x ) = 3 x 2 − 3 + 0 f ' ( x ) = 3 x 2 − 3 <

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Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3.8, Problem 33E

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The reason behind the non-working of Newton’s method for finding the root of the given equation.

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Chapter 3.8, Problem 32E

Chapter 3.8, Problem 34E

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The reason behind the non-working of Newton’s method for finding the root of the given equation.

Solution Summary: The author explains Newton's non-working method for finding the root of the given equation. The given function does not intersect the x-axis anywhere, therefore, it has no real root.

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The reason behind the non-working of Newton’s method for finding the root of the given equation.

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