Find the Slope of the Tangent Line to the Graph $f ( x ) = 4 x ^ { 3 }$

question 21

Multiple Choice

Find the slope of the tangent line to the graph of the given function $f ( x ) = 4 x ^ { 3 }$ at the point $( 2,32 )$ .

• A) \(f ^ { \prime } ( 2 ) = 96\)
• B) \(f ^ { \prime } ( 2 ) = 0\)
• C) \(f ^ { \prime } ( 2 ) = 24\)
• D) \(f ^ { \prime } ( 2 ) = 48\)
• E) \(f ^ { \prime } ( 2 ) = 16\)

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Definitions:

Marginal Rate

The rate of change in cost or benefit resulting from a particular increase in volume or activity.

Consumption

The use of goods and services by households, which is a primary component in calculating a country's gross domestic product (GDP).

Marginal Utilities

The additional satisfaction or utility gained from consuming one more unit of a good or service.

Consumption Bundle

A combination of various goods and services that an individual consumes over a given period.