Provide an Appropriate Response $F ^ { \prime } ( x )$

question 179

Multiple Choice

Provide an appropriate response.
-Find $F ^ { \prime } ( x )$ if $F ( x ) = \int _ { x } ^ { 1 } \sqrt { t ^ { 4 } + x } d t$ .

• A) \(\int _ { x } ^ { 1 } \frac { 1 } { \sqrt { t ^ { 4 } + x } } d t - \sqrt { x ^ { 4 } + x }\)
• B) \(\int _ { x } ^ { 1 } \frac { 1 } { \sqrt { t ^ { 4 } + x } } d t - x \sqrt { x ^ { 4 } + x }\)
• C) \(\int _ { x } ^ { 1 } \frac { 1 } { 2 \sqrt { t ^ { 4 } + x } } d t - \sqrt { x ^ { 4 } + x }\)
• D) \(\sqrt { x ^ { 4 } + x } - \int _ { x } ^ { 1 } \frac { 1 } { 2 \sqrt { t ^ { 4 } + x } } d t\)

Distinguish between different types of costs and their relevance to economic decision-making.

Apply the principle of marginal analysis to determine optimal levels of activity.

Understand the role of opportunity cost in comparing the value of alternate choices.

Recognize the importance of opportunity costs in resource allocation in both personal and organizational contexts.

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Definitions:

Point Estimate

A single value (statistic) given as the best guess or most reasonable approximation of a population parameter based on sample data.

Population Proportion

The fraction or percentage of members in a population that exhibit a particular characteristic or attribute.

Defective Items

Goods or products that fail to meet quality standards or specifications and are not fit for their intended use.

Independent Samples

Refers to samples drawn from distinct populations in such a way that the selection of observations in one sample does not influence the selection in another.