Locate All Inflection Points Of $f ( x ) = \frac { x } { x ^ { 2 } + 1 }$

question 3

Multiple Choice

Locate all inflection points of $f ( x ) = \frac { x } { x ^ { 2 } + 1 }$ .

• A) \(( 0,0 ) , \left( 1 , \frac { 1 } { 2 } \right) , \left( - 1 , - \frac { 1 } { 2 } \right)\)
• B)(0,0)
• C) \(( 0,0 ) , \left( - 1 , - \frac { 1 } { 2 } \right)\)
• D) \(\left( - \sqrt { 3 } , - \frac { \sqrt { 3 } } { 4 } \right) , ( 0,0 ) , \left( \sqrt { 3 } , \frac { \sqrt { 3 } } { 4 } \right)\)

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Definitions:

Price Comparison

The action of comparing prices of specific goods or services across different sellers or providers, aiming to find the most cost-effective option.

Line Segment

A part of a line that is bounded by two distinct endpoints, and contains every point on the line between its endpoints.

Producer Surplus

The difference between what producers are willing to accept for a good or service and the actual price they receive.

Price

The amount of money or value exchanged for the provision or acquisition of a good or service.