For $f ( x , y ) \text {, find all values of } x \text { and } y \text { such that } f _ { x } ( x , y ) = 0 \text { and } f _ { y } ( x , y ) = 0$

Multiple Choice

For $f ( x , y ) \text {, find all values of } x \text { and } y \text { such that } f _ { x } ( x , y ) = 0 \text { and } f _ { y } ( x , y ) = 0$ simultaneously. $f ( x , y ) = 10 x ^ { 3 } - 2 x y + 10 y ^ { 3 }$

A) $( 0,0 ) , \left( \frac { 1 } { 15 } , \frac { 1 } { 15 } \right)$
B) $\left( \frac { 1 } { 15 } , \frac { 1 } { 15 } \right)$
C) $\left( - \frac { 1 } { 15 } , - \frac { 1 } { 15 } \right) , \left( \frac { 1 } { 15 } , \frac { 1 } { 15 } \right)$
D) $\left( - \frac { 1 } { 15 } , - \frac { 1 } { 15 } \right)$
E) $( 0,0 )$