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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