Let $f ( x ) = \int _ { x ^ { 2 } } ^ { 3 } \sqrt [ 3 ] { 4 - t ^ { 3 } } d t . \text { Find } f ^ { \prime } ( x )$

question 17

Multiple Choice

Let $f ( x ) = \int _ { x ^ { 2 } } ^ { 3 } \sqrt [ 3 ] { 4 - t ^ { 3 } } d t . \text { Find } f ^ { \prime } ( x )$

• A)0
• B) \(- 2 x \sqrt [ 3 ] { 4 - x ^ { 6 } }\)
• C) \(2 x \sqrt [ 3 ] { 4 - x ^ { 6 } }\)
• D) \(\sqrt [ 3 ] { 4 - x ^ { 3 } }\)
• E) \(- \sqrt [ 3 ] { 4 - x ^ { 6 } }\)
• F)
• \(- 2 x \sqrt [ 3 ] { 4 - x ^ { 3 } }\)
• G) \(\sqrt [ 3 ] { 4 - x ^ { 6 } }\)
• H) \(- \sqrt [ 3 ] { 4 - x ^ { 3 } }\)

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Definitions:

Cross Elasticity

A measure of how the quantity demanded of one good responds to a change in the price of another good, indicating the degree of substitutability or complementarity between them.

Percentage Change

A mathematical calculation that shows how much a quantity has increased or decreased in percentage terms over a specific period.

Cross Elasticity

An indicator of the sensitivity of demand for a product to fluctuations in the price of a different product.

Antique Reproductions

Replicas or copies of antique items, often made to mimic the style and appearance of the original pieces but created with modern materials or techniques.