Question

Tìm GTLN `-4x^2+4x-3`

Answer 1

`-4x^2+4x-3`

`=-4x^2+4x-1-2`

`=-(2x-1)^2-2`

Vì `-(2x-1)^2 <= 0 AA x`

  `=>-(2x-1)^2-2 <= -2 AA x`

Hay `-4x^2 + 4x-3 <= -2 AA x`

  `=>Max =-2<=>x=1/2`

Answer 2

\(-4x^2+4x-3\)

\(=-4x^2+4x-1-2\)

\(=-\left(4x^2-4x+1\right)-2\)

\(=-\left(2x-1\right)^2-2\)

Ta thấy: \(\left(2x-1\right)^2\ge0\forall x\)

\(\Rightarrow-\left(2x-1\right)^2\le0\forall x\)

\(\Rightarrow-\left(2x-1\right)^2-2\le-2\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow2x-1=0\Leftrightarrow x=\dfrac{1}{2}\)