I have to prove that Lipschitz condition is not satisfied for the function, 

$$ f(x) =
\begin{cases}
{4x^3y \over x^4 +y^2}, & \text{if $(x,y) \neq (0,0)$ } \\
0, & \text{if $(x,y)=(0,0)$ }
\end{cases}$$

throughout any domain which includes $(0,0)$.

I considered ,the domain $D = \{(x,y) : |x| \le a , |y|\le b,a \gt b\}$, and then considered,

$$f(x,y\_1)-f(x,y\_2) = 4x^3\left[{y\_1 \over x^4+y\_1^2} - {y\_2 \over x^4+y\_2^2}\right]$$

How to proceed further?