A Function Is Given $G ( x ) = \frac { 3 } { x ^ { 2 } + x + 1 }$

question 40

Essay

A function is given.
(a) Find all the local maximum and minimum values of the function and the value of x at which each occurs.
(b) Find the intervals on which the function is increasing and on which the function is decreasing. State all answers correct to two decimal places.
$G ( x ) = \frac { 3 } { x ^ { 2 } + x + 1 }$

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Definitions:

Atherosclerosis

The buildup of fatty deposits (plaque) on the lining of arteries.

Arteries

Blood vessels that carry oxygenated blood away from the heart to the rest of the body.

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A disease characterized by the accumulation of amyloid proteins in various tissues of the body, potentially leading to organ dysfunction.

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A type of cancer that affects the blood and bone marrow, characterized by the overproduction of abnormal white blood cells.