Find the Extreme Values of the Function and Where They $$y = \frac { \ln x } { x ^ { 4 } }$$

question 51

Multiple Choice

Find the extreme values of the function and where they occur.
- $$y = \frac { \ln x } { x ^ { 4 } }$$

• A) Minimum value is \(\frac { 1 } { 4 \mathrm { e } }\) at \(\mathrm { x } = \mathrm { e } ^ { 1 / 4 }\); no maximum value.
• B) Maximum value is \(\frac { 1 } { 4 \mathrm { e } }\) at \(\mathrm { x } = \mathrm { e } ^ { 1 / 4 }\); minimum value is 0 at \(\mathrm { x } = 1\).
• C) Maximum value is \(\frac { 1 } { 4 \mathrm { e } }\) at \(\mathrm { x } = \mathrm { e } ^ { 1 / 4 }\); no minimum value.
• D) None

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Definitions:

Standard Error of Estimate

It measures the accuracy with which a sample represents a population, specifically the standard deviation of the observed values from the values predicted by a regression model.

Significance Level

The likelihood of incorrectly dismissing the null hypothesis during a statistical test when it is in fact correct; an assessment of the chance of committing a Type I error.

Negatively Linearly Related

A relationship between two variables where an increase in one variable results in a decrease in the other, represented by a downward sloping line on a graph.

Linear Relationship

A linear relationship describes a straight-line relationship between two variables, where a change in one variable is proportional to a change in the other.