Problem

Part I Multiple Choice

9. Consider the function $f(x,y)=\sqrt{|xy|}$.

(A) $f(x,y)$ is not continuous at $(0,0)$.

(B) $f(x,y)$ is continuous at $(0,0)$, but partial derivatives $f_x(0,0)$ and $f_y(0,0)$ do not exist.

(C) Both partial derivatives $f_x(0,0)$ and $f_y(0,0)$ exist, but $f(x,y)$ is not differentiable at $(0,0)$.

(D) $f(x,y)$ is differentiable at $(0,0)$.