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.
- $$f ( x , y ) = x ^ { 2 } + y ^ { 2 } , \quad x y ^ { 2 } = 2000$$

A) Maximum: none; minimum: 300 at $( 10 , \pm 10 \sqrt { 2 } )$
B) Maximum: none; minimum: 0 at $( 0,0 )$
C) Maximum: 300 at $( 10 , \pm 10 \sqrt { 2 } )$ ; minimum: 0 at $( 0,0 )$
D) Maximum: 300 at $( 10,10 \sqrt { 2 } )$ ; minimum: $- 300$ at $( 10 , - 10 \sqrt { 2 } )$