It Can Be Shown That $( 0,0 ) , ( 0,1 / 2 ) , ( 0 , - 1 / 2 ) , ( 1,0 ) , \text { and } ( - 1,0 )$

question 41

Multiple Choice

It can be shown that $( 0,0 ) , ( 0,1 / 2 ) , ( 0 , - 1 / 2 ) , ( 1,0 ) , \text { and } ( - 1,0 )$ are the critical points of the function $f ( x , y ) = \left( x ^ { 2 } + y ^ { 2 } \right) e ^ { - x ^ { 2 } - 4 y ^ { 2 } }$ .Which of the following are classified correctly? Select all that apply.

• A)(0,0)is a local minimum.
• B)(1,0)is a local maximum.
• C)(-1,0)is a local maximum.
• D) \(( 0,1 / 2 )\) is a saddle point.
• E) \(( 0 , - 1 / 2 )\) is a local minimum.

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Definitions:

Schizophrenia

A mental disorder characterized by distorted thinking, perceptions, emotions, language, sense of self, and behavior.

Hallucinations

Perceptions in the absence of external stimuli that have qualities of real perception, often seen in psychiatric conditions or drug-induced states.

Delusions

false beliefs firmly held despite clear or contradictory evidence, often seen in psychiatric conditions.

Delusions

Fixed false beliefs that are resistant to reason or confrontation with actual fact, often observed in psychiatric conditions.