Let $f ( x ) = \sqrt { x } \ln x$

question 245

Multiple Choice

Let $f ( x ) = \sqrt { x } \ln x$ . Find the interval on which $f$ is concave upward.

• A) \(( 0 , \infty )\)
• B) \(( 0,1 ]\)
• C) \([ 1 , \infty )\)
• D) \(\left( 0 , e ^ { - 1 } \right]\)
• E) \(\left[ e ^ { - 1 } , \infty \right)\)
• F) \(\left( 0 , e ^ { - 2 } \right]\)
• G) \(\left[ e ^ { - 2 } , \infty \right)\)
• H) \(( 0 , \sqrt { e } )\)

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Definitions:

Dependent Variable

The outcome variable being measured in an experiment or study, which is hypothesized to depend on or be affected by the independent variable(s).

Treatment Effectiveness

The degree to which a treatment achieves its intended outcome(s) in a real-world (clinical or practical) setting.

Between-Groups Designs

Experimental designs where different groups of participants are exposed to various conditions or treatments, allowing for comparisons between group outcomes.

Posttest-Only Control

A research design where subjects are assigned to experimental or control groups and are tested on the dependent variable only after the treatment.