Consider the function f(x,y)={x2yx2+y2if (x,y)≠(0,0)0if (x,y)=(0,0)f(x,y) = \begin{cases} \frac{x^2 y}{x^2 + y^2} & \text{if } (x,y) \neq (0,0) \\ 0 & \text{if } (x,y) = (0,0) \end{cases}f(x,y)={x2+y2x2y0if (x,y)=(0,0)if (x,y)=(0,0) Which statement about fff at the origin is TRUE?
fff is continuous but not differentiable at (0,0)(0,0)(0,0)
fff is differentiable at (0,0)(0,0)(0,0) with ∇f(0,0)=⟨0,0⟩\nabla f(0,0) = \langle 0, 0 \rangle∇f(0,0)=⟨0,0⟩
fff is not continuous at (0,0)(0,0)(0,0)
The partial derivatives fx(0,0)f_x(0,0)fx(0,0) and fy(0,0)f_y(0,0)fy(0,0) do not exist