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

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.