The Function $f ( x , y ) = x ^ { 2 } + y ^ { 2 } + 3 x y$

question 285

Multiple Choice

The function $f ( x , y ) = x ^ { 2 } + y ^ { 2 } + 3 x y$ has one critical point. Determine its location and type.

• A) \(( 2,1 )\) , saddle point
• B) \(( 2,1 )\) , minimum point
• C) \(( 2,1 )\) , maximum point
• D) \(( \sqrt { 2 } , 1 )\) , saddle point
• E) \(( \sqrt { 2 } , 1 )\) , minimum point
• F) \(( \sqrt { 2 } , 1 )\) , maximum point
• G) \(( 0,0 )\) , saddle point
• H) \(( 0,0 )\) , minimum point

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Definitions:

Reaction Time

Reaction time is the duration between the onset of a stimulus and the initiation of a response, often measured to assess sensory and cognitive processes.

Light Stimulus

A visual prompt used in experiments that involves the use of light to elicit a response from the study subject.

Margin Error

The amount of error allowed in the results of a statistical survey, reflecting the precision of the results.

Confidence Level

The probability or percentage that expresses how certain one can be about a confidence interval containing the true value of the parameter being studied.