\(B=x-x^2\)
\(=-x^2+x-1+1\)
\(=-\left(x-1\right)^2+1\)
Vì \(-\left(x-1\right)^2\le0;\forall x\)
\(\Rightarrow-\left(x-1\right)^2+1\le0+1;\forall x\)
Hay \(B\le1;\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)
Vậy MIN B=1\(\Leftrightarrow x=1\)
B = x - x2
B = - ( x2 - 2x.2 + 22 - 4 )
B = - [ ( x - 2 )2 - 4 ]
B = - ( x - 2 )2 +4
Vì \(-\left(x-2\right)^2\le0\forall x\)
\(\Rightarrow-\left(x-2\right)^2+4\le4\)
Dấu " = " xảy ra khi :
- ( x - 2 )2 = 0
x - 2 = 0
x = 2
Vậy Max A = 4 <=> x = 2
C = 2x - 2x2 - 5
C = - ( 2x2 - 2x + 5 )
C = - [ ( x - 1 )2 + x2 + 4 ]
C = - ( x -1 )2 - x2 - 4
Vì \(\orbr{\begin{cases}-\left(x-1\right)^2\le0\\-x^2\le0\end{cases}}\Rightarrow-\left(x-1\right)^2-x^2-4\le-4\)
Dấu " = " xảy ra khi
- x2 = 0
x = 0
Hoặc
- ( x - 1 )2 = 0
x = 1
Vậy Max A = -4 <=> x = 0 hoặc x = 1
Chắc vậy
hok tốt
\(C=2x-2x^2-5\)
\(=-\left(2x^2-2x+5\right)\)
\(=-\left(2x^2-2.x\sqrt{2}.\frac{2}{2\sqrt{2}}+\frac{1}{2}-\frac{1}{2}+5\right)\)
\(=-\left[\left(x\sqrt{2}-\frac{1}{2}\right)^2+\frac{9}{2}\right]\)
\(=-\left(x\sqrt{2}-\frac{1}{2}\right)^2-\frac{9}{2}\)
Vì \(-\left(x\sqrt{2}-\frac{1}{2}\right)^2\le0;\forall x\)
\(\Rightarrow-\left(x\sqrt{2}-\frac{1}{2}\right)^2-\frac{9}{2}\le0-\frac{9}{2};\forall x\)
Hay \(C\le\frac{-9}{2};\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x\sqrt{2}-\frac{1}{2}=0\)
\(\Leftrightarrow x=\frac{\sqrt{2}}{4}\)
Vậy MIN \(B=\frac{-9}{2}\)\(\Leftrightarrow x=\frac{\sqrt{2}}{4}\)
Nhưng mà bài tui câu B sai nha -.-
Xin lỗi
B = x - x2
B = - ( x2 - 2x.\(\frac{1}{2}\)+\(\left(\frac{1}{2}\right)^2\)- 0,75 )
B = - [ ( x - \(\frac{1}{2}\))2 + 0,745 )
B = - ( x - \(\frac{1}{2}\)) + 0,75
Vì \(-\left(x-\frac{1}{2}\right)^2\le0\forall x\)
=> \(-\left(x-\frac{1}{2}\right)^2+0,75\le0,75\)
Dấu " = : xảy ra khi ;
\(-\left(x-\frac{1}{2}\right)^2=0\)
=> x = \(\frac{1}{2}\)
Vậy Max B = 0, 75 ,=> x = \(\frac{1}{2}\)
