Question

defined by $f\left(x\right)=\left\{\begin{array}{c}k-2x,ifx\le 1\\ 2x+3,ifx>-1\end{array}\right\}$,if has a local minimum at x= -1, then a pair

Answer 1

$\begin{array}{c}f\left(x\right)\left\{\begin{array}{c}k-2x,ifx\le 1\\ 2x+3,ifx>-1\end{array}\right\}\\ f\left(1^{-}\right)=f\left(1-n\right)=k-2\left(1-h\right)=k-2\\ \Rightarrow f\left(1^{+}\right)\\ {lim}_{x\to 1}=f\left(1+n\right)={lim}_{x\to 1}=2\left(1+h\right)+3={lim}_{x\to 1}=2+2h+3=5\\ then,\\ f\left(1\right)=f\left(1^{-}\right)=f\left(1^{+}\right)=5\\ \therefore k-2=5,k=7\end{array}$