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

question 140

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 \(\left( 1 , \frac { 8 } { 7 } \right)\)

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