In this way, you can test four options and know the answer.

The second derivative of A f about y is 2, and the first derivative of f about y is 2y -x x. If y=0, the result is -x, no,

The second derivative of B f about y is 2, and the first derivative of f about y is 2y+x. If y=0, the result is x, right.

The second derivative of C f about y is 2, and the first derivative of f about y is 2y-x 2. If y=0, the result is-x 2, which is wrong.

The second derivative of D f about y is 2, and the first derivative of f about y is 2y+x 2. If y=0, the result is x 2, no,

So the answer is B.