If $g ( x ) = \sqrt { 2 - 3 x }$

question 82

Multiple Choice

If $g ( x ) = \sqrt { 2 - 3 x }$ , use the definition of derivative to find $g ^ { \prime } ( x )$

• A)
• \(g ^ { \prime } ( x ) = - \frac { 1 } { 2 } ( 2 - 3 x ) ^ { - 1 / 2 }\)
• B) \(g ^ { \prime } ( x ) = - ( 2 - 3 x ) ^ { - 1 / 2 }\)
• C)
• \(g ^ { \prime } ( x ) = - \frac { 3 } { 2 } ( 2 - 3 x ) ^ { 1 / 2 }\)
• D)
• \[g ^ { \prime } ( x ) = - \frac { 3 } { 2 } ( 2 - 3 x ) ^ { - 1 / 2 }\]
• E) None of these

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Definitions:

Perfectly Competitive

A market structure characterized by a large number of buyers and sellers, homogenous products, and no barriers to entry or exit.

Duopoly Market

A market structure dominated by only two producers or sellers, leading to a form of competition that significantly impacts pricing and output decisions.

Merging Firms

The process where two or more companies combine into a single company, often to expand market share, reduce costs, or increase competitiveness.

Identical Product

A product that is exactly the same in every feature, quality, and production process with another product, making them interchangeable.