Solve the Problem $$f ( x ) = x ^ { 3 }$$

question 132

Multiple Choice

Solve the problem.
-The function f $$f ( x ) = x ^ { 3 }$$ describes the volume of a cube, f(x) , in cubic inches, whose length, width, and height each measure x inches. Find the instantaneous rate of change of the volume with respect to x when x = 4 inches.

• A) 12 cubic inches per inch
• B) 49.21 cubic inches per inch
• C) 48 cubic inches per inch
• D) 192 cubic inches per inch

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Definitions:

Marginal Utility

The additional satisfaction or utility received by consuming one more unit of a good or service.

Total Utility

The overall pleasure or value derived by using a certain amount of an item or service.

Marginal Utility

The extra pleasure or benefit a buyer receives from purchasing an additional unit of a product or service.

Total Utility

The overall satisfaction or fulfillment a consumer derives from consuming a particular quantity of goods or services.