Provide an Appropriate Response $\mathrm { f } ( \mathrm { x } , \mathrm { y } )$

Multiple Choice

Provide an appropriate response.
-Find any local extrema (maxima, minima, or saddle points) of $\mathrm { f } ( \mathrm { x } , \mathrm { y } )$ given that $\mathrm { f } _ { \mathrm { x } } = 5 \mathrm { x } + 5 \mathrm { y }$ and $\mathrm { f } _ { \mathrm { y } } = 3 \mathrm { x } - 8 \mathrm { y }$ .

A) Local maximum at $\left( - 1 , \frac { 8 } { 3 } \right)$
B) Saddle point at $( - 40,15 )$
C) Saddle point at $( 0,0 )$
D) Local minimum at $\left( - 1 , \frac { 8 } { 3 } \right)$