Find the Extreme Values of the Function Subject to the Given

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y ) = x ^ { 2 } y , x ^ { 2 } + 2 y ^ { 2 } = 6$$

A) Maximum: 4 at $( 2,1 )$ ; minimum: $- 4$ at $( - 2 , - 1 )$
B) Maximum: 18 at $( \pm 3,2 )$ ; minimum: $- 18$ at $( \pm 3 , - 2 )$
C) Maximum: 4 at $( \pm 2,1 )$ ; minimum: $- 4$ at $( \pm 2 , - 1 )$
D) Maximum: 18 at $( 3,2 )$ ; minimum: $- 18$ at $( - 3 , - 2 )$