= -2( x2 +2x/2 +1/4) +5 + 1/2
= -2(x+1/2)2 + 5,5
GTLN = 5,5
mk làm tắt giỏi toán moi hieu
\(-2x^2+x+5=-2\left(x^2-\frac{x}{2}\right)+5=-2\left(x^2-2.x.\frac{1}{4}+\frac{1}{16}\right)+\frac{1}{8}+5=-2\left(x-\frac{1}{4}\right)^2+\frac{41}{8}\le\frac{41}{8}\)Do đó Max = \(\frac{41}{8}\Leftrightarrow x=\frac{1}{4}\)
\(-2\left(x^2-\frac{1}{2}x-\frac{5}{2}\right)\)
\(\Leftrightarrow-2\left(x^2-2.x\frac{1}{4}+\frac{1}{16}-\frac{5}{2}-\frac{1}{16}\right)\)
\(\Leftrightarrow-2\left[\left(x-\frac{1}{4}\right)^2-\frac{41}{16}\right]\)
\(\Leftrightarrow-2\left(x-\frac{1}{4}\right)^2+\frac{41}{8}\le\frac{41}{8}\)
Vậy \(\left(-2x^2+x+5\right)_{max}\)khi \(x-\frac{1}{4}=0\Rightarrow x=\frac{1}{4}\)
