Solve the Problem $x _ { 0 }$ That Lies at a Critical Point

question 396

Essay

Solve the problem.
-Suppose Newton's Method is used with an initial guess $x _ { 0 }$ that lies at a critical point $( a , b ) , b \neq 0$ . What happens to $x _ { 1 }$ and later approximations? Give reasons for your answer.

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Definitions:

Mudsill

A derogatory term historically used to refer to the lowest class of workers, particularly in the Southern United States, suggesting a foundation that others build upon but do not acknowledge.

South Carolina

A state located in the southeastern United States, known for its historic cities, coastal landscapes, and as an early adopter of the Articles of Confederation.

Slavery

The condition in which individuals are owned by others, who control where they live and at what they work.

Vigilance Societies

Groups formed by private citizens to act as self-appointed law enforcement to protect community interests, often present in areas where they perceived official law enforcement as inadequate.