\(A=2+x-x^2\)
\(=-\left(x^2-2.x.\frac{1}{2}+\frac{1}{4}-\frac{1}{4}-2\right)\)
\(=-\left(x-\frac{1}{2}\right)^2+\frac{9}{4}\)
Vì \(-\left(x-\frac{1}{2}\right)^2\le0;\forall x\)
\(\Rightarrow-\left(x-\frac{1}{2}\right)^2+\frac{9}{4}\le0+\frac{9}{4};\forall x\)
Hay \(A\le\frac{9}{4};\forall x\)
Dấu "="xảy ra \(\Leftrightarrow\left(x-\frac{1}{2}\right)^2=0\)
\(\Leftrightarrow x=\frac{1}{2}\)
Vậy MAX \(A=\frac{9}{4}\)\(\Leftrightarrow x=\frac{1}{2}\)
\(B=x^2-4x+1\)
\(=\left(x-2\right)^2-3\)
Vì \(\left(x-2\right)^2\ge0;\forall x\)
\(\Rightarrow\left(x-2\right)^2-3\ge0-3;\forall x\)
Hay \(B\ge-3;\forall x\)
Dấu "="xảy ra \(\Leftrightarrow\left(x-2\right)^2=0\)
\(\Leftrightarrow x=2\)
Vậy \(B_{min}=-3\Leftrightarrow x=2\)
Z 