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

question 14

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 each answer correct to two decimal places. $G ( x ) = \frac { 2 } { x ^ { 2 } + x + 1 }$

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Definitions:

Scattergraph

A graphical method used to display the relationship between two quantitative variables, often used to identify trends or patterns.

Least Squares Regression

A statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables by minimizing the sum of the squares of the differences between the observed and predicted values.

Variable Manufacturing Cost

Costs that vary with production volume, including direct materials, direct labor, and certain overheads.

Production Volume

The total quantity of units produced during a specific period.