Cubics over quadratics at the origin

Let $f:\mathbb{R}^{2}\to\mathbb{R}$ be defined by $$f(x,y)=\begin{cases}\dfrac{2x^{3}+3y^{3}}{x^{2}+y^{2}},&(x,y)\neq(0,0),\\0,&(x,y)=(0,0).\end{cases}$$ Let $f_{x}(0,0)$ and $f_{y}(0,0)$ denote the first order partial derivatives of $f(x,y)$ with respect to $x$ and $y$, respectively, at the point $(0,0)$. Then which one of the following statements is TRUE?