\(f\left(x\right)=x^2-2x+3=x\left(x-2\right)+3\)
Do \(x\in\left[-2;0\right]\) nên \(\left\{{}\begin{matrix}x\le0\\x-2< 0\end{matrix}\right.\) \(\Rightarrow x\left(x-2\right)\ge0\)
\(\Rightarrow f\left(x\right)\ge3\)
\(\Rightarrow\min\limits_{x\in\left[-2;0\right]}f\left(x\right)=3\) khi \(x=0\)
\(f\left(x\right)=x^2-2x+3=x^2-2x-8+11=\left(x+2\right)\left(x-4\right)+11\)
Do \(x\in\left[-2;0\right]\Rightarrow\left\{{}\begin{matrix}x+2\ge0\\x-4< 0\end{matrix}\right.\) \(\Rightarrow\left(x+2\right)\left(x-4\right)\le0\)
\(\Rightarrow f\left(x\right)\le11\)
\(\Rightarrow\max\limits_{x\in\left[-2;0\right]}f\left(x\right)=11\) khi \(x=-2\)
