Use Newton's Method to Find the Point on the Graph $f ( x ) = 4 - x ^ { 2 }$

question 27

Multiple Choice

Use Newton's Method to find the point on the graph of $f ( x ) = 4 - x ^ { 2 }$ that is closest to the point $( 1,0 )$ . Round your answer to three decimal places.

• A) \(( 1.926,0.291 )\)
• B) \(( 2.485,0.291 )\)
• C) \(( 1.926,1.526 )\)
• D) \(( 0.670,0.291 )\)
• E) \(( 1.926 , - 2.27 )\)

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Definitions:

Benzene

An aromatic hydrocarbon with a ring of six carbon atoms bonded together in a planar hexagonal ring with alternating single and double bonds.

Bromination

A chemical reaction involving the addition or substitution of bromine to an organic compound, often used in synthesis.

Mononitration

The chemical process of introducing one nitro group (-NO2) to a molecule, commonly used in the synthesis of explosives and various organic compounds.

Major Organic Product

The main product produced in the greatest amount when organic compounds undergo a chemical reaction.