Provide an Appropriate Response $f ( x , y )$ Given That

Provide an appropriate response.
-Find any local extrema (maxima, minima, or saddle points) of $f ( x , y )$ given that $\mathrm { f } _ { \mathrm { X } } = 8 \mathrm { x } - 4 \mathrm { y }$ and $\mathrm { f } _ { \mathrm { y } } = - 8 \mathrm { x } + 6 \mathrm { y }$ .

A) Local maximum at $\left( \frac { 1 } { 2 } , \frac { 3 } { 4 } \right)$
B) Local minimum at $\left( \frac { 1 } { 2 } , \frac { 3 } { 4 } \right)$
C) Local minimum at $( 0,0 )$
D) Saddle point at $( 0,0 )$