함수 $f \left (x, y \right) =y^3 +3x^2 y-6x^2 -6y^2 +2$ 의 극댓값, 극솟값, 안장점의 위치를 순서대로 나열한 것은?

• ①$\left (4, 0 \right), \left (0, 0 \right), \left (2, -2 \right)$
• ②$\left (0, 0 \right), \left (0, 4 \right), \left (2, 2 \right)$
• ③$\left (4, 0 \right), \left (0, 4 \right), \left (2, 2 \right)$
• ④$\left (0, 0 \right), \left (0, 4 \right), \left (2, -2 \right)$
• ⑤$\left (4, 0 \right), \left (0, 4 \right), \left (2, -2 \right)$