Identify the Function's Local and Absolute Extreme Values, If Any $$g ( x ) = \frac { x ^ { 4 } } { 4 } - \frac { 4 } { 3 } x ^ { 3 } - \frac { 9 } { 2 } x ^ { 2 } + 36 x - 4$$

question 331

Multiple Choice

Identify the function's local and absolute extreme values, if any, saying where they occur.
- $$g ( x ) = \frac { x ^ { 4 } } { 4 } - \frac { 4 } { 3 } x ^ { 3 } - \frac { 9 } { 2 } x ^ { 2 } + 36 x - 4$$

• A) local maxima at x = 3 and x = -4; local minimum at x = 3
• B) local maximum at x = 3; local minima at x = -3 and x = 4
• C) local maxima at x = -3 and x = 4; local minimum at x = 3
• D) local maximum at x = -3; local minimum at x = 4

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Definitions:

MC = MR

A condition where a firm's marginal cost (MC) of producing an additional unit is equal to its marginal revenue (MR) from selling that unit, often used to determine the profit-maximizing level of production.

Costs Of Production

Costs of production refer to the total expenses incurred in the manufacturing of a product, including raw materials, labor, and overhead.

Marginal Revenue

The additional income received from selling one more unit of a product or service.

Marginal Cost

The expenditure required to create another single unit of a good or service.