1) \(A=x^2-6x+11=\left(x^2-6x+9\right)+2\)
\(=\left(x-3\right)^2+2\ge2\)
\(minA=2\Leftrightarrow x=3\)
2) \(B=2x^2+10x-1=2\left(x^2+5x+\dfrac{25}{4}\right)-\dfrac{27}{2}\)
\(=2\left(x+\dfrac{5}{2}\right)^2-\dfrac{27}{2}\ge-\dfrac{27}{2}\)
\(minB=-\dfrac{27}{2}\Leftrightarrow x=-\dfrac{5}{2}\)
3) \(C=5x-x^2=-\left(x^2-5x+\dfrac{25}{4}\right)+\dfrac{25}{4}\)
\(=-\left(x-\dfrac{5}{2}\right)^2+\dfrac{25}{4}\le\dfrac{25}{4}\)
\(maxC=\dfrac{25}{4}\Leftrightarrow x=\dfrac{5}{2}\)
4) \(D=-8x^2+6\le6\)
\(maxD=6\Leftrightarrow x=0\)
1) A=x2−6x+11=(x2−6x+9)+2A=x2−6x+11=(x2−6x+9)+2
=(x−3)2+2≥2=(x−3)2+2≥2
minA=2⇔x=3minA=2⇔x=3
2) =2(x+52)2−272≥−272=2(x+52)2−272≥−272
C=5x−x2=−(x2−5x+254)+254C=5x−x2=−(x2−5x+254)+254
maxC=254⇔x=52maxC=254⇔x=52
4) D=−8x2+6≤6D=−8x2+6≤6
maxD=6⇔x=0
