Find the Extreme Values of the Function Subject to the Given

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 $\left( - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right)$