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 a possible value of k is

• A. 0
• B. $-\frac{1}{2}$
• C. -1
• D. 1

Answer 1

The correct option is C -1

$f\left(x\right)=\{\begin{array}{c}k-2x,ifx\le -1\\ 2x+3,ifx>-1\end{array}$

$\underset{x\to -1^2}{lim}k-2x=\underset{x\to -1^{+}}{lim}2x+3$

$k+2=-2+3$

$k=-1$