Examine the Function $f ( x , y ) = 5 x ^ { 2 } - 8 y ^ { 2 } - 3 x + 8 y + 4$

Multiple Choice

Examine the function $f ( x , y ) = 5 x ^ { 2 } - 8 y ^ { 2 } - 3 x + 8 y + 4$ for relative extrema.

A) saddle point at $\left( \frac { 3 } { 10 } , \frac { 1 } { 2 } \right)$
B) relative minimum at $\left( \frac { 3 } { 10 } , \frac { 1 } { 2 } \right)$
C) saddle point at $\left( - \frac { 3 } { 10 } , \frac { 1 } { 2 } \right)$
D) relative maximum at $\left( \frac { 3 } { 10 } , - \frac { 1 } { 2 } \right)$
E) saddle point at $\left( - \frac { 3 } { 10 } , - \frac { 1 } { 2 } \right)$