Do a sketch of $f$ with the equation $f(x,y)=0$. Give in all non singular points of the curve a normal vector.
$f(x,y)=x^{3}-x-y$
How can I do this thing with normal vector? I know that singular points are when gradient of function is $0$ and I just put this equation in wolframalpha and got a plot, but I dont know should I do that on that way and what to do with normal vector?
I do not want to spoiler too much, so take this hint: [EDIT: i spoilered in the comments]
if you have a curve $\gamma$ in the set $\left\{\left(x,y\right)|f\left(x,y\right)=0\right\}$ what can you say about $\frac{\partial}{\partial t}\left(f\left(\gamma\left(t\right)\right)\right)$?
(a curve is in this case a map $t\stackrel{\gamma}{\mapsto}\left(\gamma_x\left(t\right),\gamma_y\left(t\right)\right)\in\mathbb{R}^2$)