The function fx y xy sin1xwhen x 0 and f0 y 0a has both

Question

The function f(x, y) = xy sin(1/x)

when (x =| 0), and f(0, y) = 0

(A) has both partial derivatives at (0; 1). (B) is dierentiable at (0; 0) and discontinuous at (1; 0).

(C) is continuous at (1; 0) and dierentiable (D) is continuous at (0; 0) and dierentiable at (1; 0).

everywhere in R2. (E) none of the above.