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:

Medical Asepsis

Practices aimed at reducing the number and spread of pathogens to prevent infection, commonly known as clean techniques.

Antiseptic

Substances used on the skin or living tissues to inhibit the growth of microorganisms.

Sterile Drape

A sterile covering used in surgical procedures to prevent contamination of the surgical site.

Hand Antiseptics

Products used to cleanse hands, killing or inhibiting the growth of microorganisms to prevent infection.