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

Multiple Choice

Provide an appropriate response.
-Find any local extrema (maxima, minima, or saddle points) of $f ( x , y )$ given that $\mathrm { f } _ { \mathrm { x } } = - 4 \mathrm { x } + 4 \mathrm { y }$ and $\mathrm { f } _ { \mathrm { y } } = 7 \mathrm { x } - 8 \mathrm { y }$ .

A) Local maximum at $( 0,0 )$
B) Saddle point at $( 0,0 )$
C) Local maximum at $\left( 1 , \frac { 8 } { 7 } \right)$
D) Local minimum at $\left( 1 , \frac { 8 } { 7 } \right)$