Find the Extreme Values of the Function Subject to the Given

question 314

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $f ( x , y ) = 3 x - y + 1 , \quad 3 x ^ { 2 } + y ^ { 2 } = 9$

• A) Maximum: 7 at \(\left( \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right) ;\) minimum: \(- 5\) at \(\left( - \frac { 3 } { 2 } , \frac { 3 } { 2 } \right)\)
• B) Maximum: 4 at \(\left( \frac { 3 } { 2 } , \frac { 3 } { 2 } \right) ;\) minimum: \(- 2\) at \(\left( - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right)\)
• C) Maximum: 4 at \(\left( \frac { 3 } { 2 } , \frac { 3 } { 2 } \right) ;\) minimum: \(- 5\) at \(\left( - \frac { 3 } { 2 } , \frac { 3 } { 2 } \right)\)
• D) Maximum: 7 at \(\left( \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right) ;\) minimum: \(- 2\) at \(\left( - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right)\)