A cone is a set that is closed under multiplication by positive scalars. The tangent cone of $f$ at $x$ is defined as the set of descent directions of $f$ at $x$ $$\mathcal{T}_f(\boldsymbol{x})=\{\boldsymbol{u}\in\mathbb{R}^n: f(\boldsymbol{x}+t\cdot\boldsymbol{u})\le f(\boldsymbol{x}) \ \text{for some}\ t>0 \}$$.
The problem is, how can I get the tangent cone of $f(\boldsymbol{x})=||\boldsymbol{x}||_1$ at point $\boldsymbol{x}=(1,0)$?
Adding: the picture of $f(\boldsymbol{x})=||\boldsymbol{x}||_1$ is enter image description here
I think I get a new understanding of tangent cone, is the tangent cone of $y=|x|$ at $(0,0)$ as the following picture?
