The problem at hand is the following: Consider the set $S =\{(x,y)\in\mathbb{R^2} : y^2\le x\le y \}$. Draw the set $S$ and the set of all feasible directions at $(1,1)$.
I tried to use the definition of feasible directions (for a given point $a\in S$ we call a direction $d\neq 0$ feasible if $a+td\in S$ for $0\le t\le \delta $ if $\delta\gt 0$ is small enough).
I also tried to use the fact that $d^T\nabla g(1,1)\le 0$.
Could you please help me figure out how they got to the following answer: The set of all feasible directions at $(1,1)$ is $S =\{(x,y)\in R^2 : x\le y\lt x/2 \}$