\(E=5-8x-x^2\)
\(=-\left(x^2+8x+16\right)+21\)
\(=-\left(x+4\right)^2+21\)
Ta có :\(-\left(x+4\right)^2\le0\Rightarrow-\left(x+4\right)^2+21\le21\)
Dấu = xảy ra \(\Leftrightarrow x+4=0\Leftrightarrow x=-4\)
Vậy \(Max_E=21\Leftrightarrow x=-4\)
\(F=4x-x^2+1\)
\(=-\left(x^2-4x+4\right)+5\)
\(=-\left(x-2\right)^2+5\)
Ta có :\(-\left(x-2\right)^2\le0\Rightarrow-\left(x-2\right)^2+5\le5\)
Dấu = xảy ra \(\Leftrightarrow x-2=0\Leftrightarrow x=2\)
Vậy \(Max_E=5\Leftrightarrow x=2\)
Ta có: \(E=5-8x-x^2=-x^2-8x+5=-x^2-2.4.x+16-11\)
\(=-\left(x-4\right)^2-11\le0-11=-11\)
Dấu "=" xảy ra \(\Leftrightarrow-\left(x-4\right)^2=0\)
\(\Rightarrow x-4=0\)
\(\Rightarrow x=4\)
Vậy GTLN của E là -11 \(\Leftrightarrow x=4\)
Ta có: \(F=4x-x^2+1=-x^2+4x+1=-x^2+2.2.x+4-3\)
\(=-\left(x+2\right)^2-3\le0-3=-3\)
Dấu "=" xảy ra \(\Leftrightarrow-\left(x+2\right)^2=0\)
\(\Rightarrow x+2=0\)
\(\Rightarrow x=-2\)
Vậy GTLN của F là -3 \(\Leftrightarrow x=-2\)
