Determine Where the Graph of the Function $f ( x ) = x ^ { 3 } - 6 x$

question 37

Multiple Choice

Determine where the graph of the function $f ( x ) = x ^ { 3 } - 6 x$ is concave upward and where it is concave downward. Also, find all inflection points of the function.

• A) \(\mathrm { CU }\) on \(( \sqrt { 2 } , \infty ) , \mathrm { CD }\) on \(( - \infty , \sqrt { 2 } )\),
• IP \(( \sqrt { 2 } , - 4 \sqrt { 2 } )\)
• B) \(\mathrm { CU }\) on \(( - \sqrt { 2 } , \sqrt { 2 } ) , \mathrm { CD }\) on \(( - \infty , - \sqrt { 2 } )\) and \(( \sqrt { 2 } , \infty )\)
• IP \(( - \sqrt { 2 } , 4 \sqrt { 2 } )\) and \(( \sqrt { 2 } , - 4 \sqrt { 2 } )\)
• C) \(\mathrm { CU }\) on \(( 0 , \infty ) , \mathrm { CD }\) on \(( - \infty , 0 )\),
• IP \(( 0,0 )\)
• D) \(\operatorname { CU }\) on \(( - \sqrt { 2 } , \infty ) , \mathrm { CD }\) on \(( - \infty , - \sqrt { 2 } )\),
• IP \(( - \sqrt { 2 } , 4 \sqrt { 2 } )\)

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Definitions:

Excitatory

Refers to the process or substances that increase nerve signal transmission and promote neural activity.

Voice Onset Times

The time delay between the beginning of the pronunciation of a consonant and the start of the vibration of the vocal cords.

Computer-Generated Syllables

Artificially produced sounds or combinations of sounds that mimic elements of human speech, often used in research or technological applications.

Consonant Sounds

The sounds produced by blocking the air flow through the mouth using the lips, teeth, or palate, distinguished from vowels.