Let $f: R \rightarrow R$ be defined by
$f(x)=\left\{\begin{array}{l}
k-2 x, \text { if } x \leq-1 \\
2 x+3, \text { if } x>-1
\end{array}\right.$
If f has a local minimum at $x=-1$, then a possible value of $k$, is
Answer & explanation
Correct answer: option 2
If $f(x)$ has a local minimum at $x=-1$, then
$\lim\limits_{x \rightarrow-1^{+}} f(x)=\lim\limits_{x \rightarrow-1^{-}} f(x)$
$\Rightarrow \lim\limits_{x \rightarrow-1^{+}} 2 x+3=\lim\limits_{x \rightarrow-1^{-}} k-2 x$
$\Rightarrow -2+3=k+2 \Rightarrow k=-1$
