Expand the Expression in the Difference Quotient and Simplify $\frac { f ( x + h ) - f ( x ) } { h }$

question 128

Multiple Choice

Expand the expression in the difference quotient and simplify. $\frac { f ( x + h ) - f ( x ) } { h }$ Difference quotient $f ( x ) = ( x ) ^ { 3 }$

• A) \(\frac { 3 x ^ { 2 } + 3 x h + h ^ { 2 } } { h }\)
• B) \(3 x ^ { 2 } - 3 x h - h ^ { 2 }\)
• C) \(\frac { 3 x ^ { 2 } + 3 x h - h ^ { 2 } } { h }\)
• D) \(3 x ^ { 2 } + 3 x h - h ^ { 2 }\)
• E) \(3 x ^ { 2 } + 3 x h + h ^ { 2 }\)

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Definitions:

Government Failure

Situations where government intervention in the economy creates inefficiencies or worsens outcomes.

Efficient Allocation

The optimal distribution of resources among competing entities to achieve the desired outcomes with minimal waste or inefficiency.

Government Failure

Occurs when government intervention in the economy causes more harm than good, leading to inefficiencies or unintended negative consequences.

Idealized Economic Efficiency

A theoretical state in which resources are allocated in the most effective way possible, maximizing productivity while minimizing waste and inefficiencies.