Locate the local maximum of the function. $f ( x , y ) = x ^ { 2 } y - 8 x ^ { 2 } - 4 y ^ { 2 }$
A) $( 8,4 , - 256 )$
B) $( 0,0,0 )$
C) $( - 8,8 , - 256 )$
D) $( - 8 , - 4,0 )$
E) $( 8,8 , - 256 )$

Question

Locate the local maximum of the function.   $f ( x , y ) = x ^ { 2 } y - 8 x ^ { 2 } - 4 y ^ { 2 }$  
A) $( 8,4 , - 256 )$
B) $( 0,0,0 )$
C) $( - 8,8 , - 256 )$
D) $( - 8 , - 4,0 )$
E) $( 8,8 , - 256 )$

Quizplus · Accepted Answer

The function has a local maximum at the origin $(0,0)$ because the second derivative test shows that the critical point at $(0,0)$ is a local maximum.

Locate the Local Maximum of the Function f(x,y)=x2y−8x2−4y2f ( x , y ) = x ^ { 2 } y - 8 x ^ { 2 } - 4 y ^ { 2 }f(x,y)=x2y−8x2−4y2

Locate the Local Maximum of the Function $f ( x , y ) = x ^ { 2 } y - 8 x ^ { 2 } - 4 y ^ { 2 }$