Problem in op. d

Q.14 Letf: RË > R be defined by 2x Tay)=rtya ,) * (0.0) y) = (0,0) Let f (0,0) and ,(0,0) denote the first order partial derivatives of fa.y) with respect to X and y, respectively, at the point (0,0). Then which one of the following statements is TRUE? (A)fis continuous at (0,0) but f(0,0) and f,0,0) do not exist (B) f is differentiable at (0,0) (C)fis not differentiable at (0,0) D) fis not continuous at (0, 0) but E(0, 0) and y(0,0) exist