Find the Linearization $L ( x )$ Of the Function At $a$

question 42

Multiple Choice

Find the linearization $L ( x )$ of the function at $a$ .
$f ( x ) = x ^ { 2 / 3 } ; \quad a = 64$

• A) \(\frac { 8 } { 3 } x + \frac { 464 } { 3 }\)
• B) \(\frac { 8 } { 3 } x + \frac { 512 } { 3 }\)
• C) \(\frac { 8 } { 3 } x - \frac { 512 } { 3 }\)
• D) \(\frac { 8 } { 3 } x - \frac { 464 } { 3 }\)

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Definitions:

Direction Of Rotation

The clockwise or counterclockwise movement of a mechanical component or system as seen from a specific vantage point.

Drive Gear

Any gear that drives another.

Torque Reduction

A process or mechanism by which torque output, particularly in an engine or drivetrain, is intentionally decreased to prevent damage or improve control.

Driven Gear

A gear that receives power from another gear or rotating component in a mechanical system.