Let $f:\mathbb{R}\to \mathbb{R}$ be defined by $f(x)=\{\begin{array}{ll}k-2x,& \text{if }x\le -1\\ 2x+3,& \text{if }x>-1\end{array}$. If $f$ has a local minimum at $x=-1$, then a possible value of $k$ is:

For a local minimum at $x=-1$, the function value $f(-1)$ must be less than or equal to the limit as $x\to -1^{+}$.$f(-1)=k-2(-1)=k+2$.${\lim }_{x\to -1^{+}}f(x)=2(-1)+3=1$.For local minimum: $k+2\le 1⟹k\le -1$.Among the options, $k=-1$ is a possible value.