9. let f:r° >r be defined by tla,y)=+ y f a,y) a (0,0), 0 if (x,y) = (0,0). which of the following statements holds regarding the continuity and the existence o

9. Let f:R° >R be defined by Tla,y)=+ y f a,y) a (0,0), 0 if (x,y) = (0,0). Which of the following statements holds regarding the continuity and the existence of partial derivatives of f at (0,0)? (A) Both partial derivatives of f exist at (0,0) and f is continuous at (0,0) 5 (B) Both partial derivatives of f exist at (0,0) and f is NOT continuous at (0,0) (C)One partial derivative of f does NOT exist at (0,0) and f is continuous at (0,0) (D) One partial derivative of f does NOT exist at (0,0) and f is NOT continuous at (0,0)