Question

Let $f:R\to R$ be defined by
$f\left(x\right)=\{\begin{array}{c}k-2x,ifx\le -1\\ 2x+3,ifx>-1\end{array}$
If $f$ has a local minimum at $x=-1$, then the possible value of $k$ is

• A. $-1/2$
• B. $-1$
• C. $1$
• D. $0$

Answer 1

Answer: (B)

$-1$

$f\left(x\right)$ has local minimum at $x=-1\Rightarrow f\left(x\right)$ should continuous at $x=-1$

$\Rightarrow f(-1)=\underset{x\to -1^{+}}{lim}f\left(x\right)$

$\Rightarrow k+2=2(-1)+3=1$

$k=-1$