Let $f:R \to R$ be defined by $$$f\left( x \right) = \left\{ {\matrix{ {k - 2x,\,\,if} & {x \le - 1} \cr {2x + 3,\,\,if} & {x > - 1} \cr } } \right.$$$ If $f$has a local minimum at $x=-1$, then a possible value of $k$ is

Question

Let $f:R \to R$ be defined by $$$f\left( x \right) = \left\{ {\matrix{ {k - 2x,\,\,if} & {x \le - 1} \cr {2x + 3,\,\,if} & {x > - 1} \cr } } \right.$$$

If $f$has a local minimum at $x=-1$, then a possible value of $k$ is

$0$

$ - {1 \over 2}$

$-1$

$1$

Solution

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