Find the Minimum and Maximum Value Of $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$

Multiple Choice

Find the minimum and maximum value of $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$ on the ellipse $3 x ^ { 2 } + 2 y ^ { 2 } = 1$ .

A) Minimum $\frac { 1 } { 4 }$ , maximum $\frac { 5 } { 12 }$
B) Minimum $\frac { 1 } { 3 }$ , maximum $\frac { 1 } { 2 }$
C) Minimum $\frac { 1 } { 6 }$ , maximum $\frac { 5 } { 6 }$
D) No maximum or minimum, unbounded