Find the Linearization L (X) of the Function at A f

question 91

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:

Equilibrium Quantity

The amount of goods or services supplied and demanded at the equilibrium price.

Bushels

A unit of volume that is used primarily in the United States to measure agricultural commodities, like grains and fruits.

Shortage

A situation in which the demand for a good or service exceeds its supply at a particular price.

Surplus

An excess of production or supply over demand, often leading to a decrease in prices.