`1)A=-9x²+7x+2`
`=-(9x²-7x-2)`
`=-(9x²-7x+49/36-121/36)`
`=-(9x²-7x+49/36)+121/36`
`=-[(3x)²-2.3x. 7/6+(7/6)^2]+121/36`
`=-(3x-7/6)^2+121/36`
Ta có:`(3x-7/6)^2≥0∀x`
`⇒-(3x-7/6)^2≤0∀x`
`⇒-(3x-7/6)^2+121/36≤121/36`
Dấu `'='` xảy ra khi `3x-7/6=0⇔3x=7/6⇔x=7/18`
Vậy `A_(max)=121/36` khi `x=7/18`
`2)B=-5x²+x-2`
`=-(5x²-x+2)`
`=-5(x²-1/5x+2/5)`
`=-5(x²-1/5x+1/100+39/100)`
`=-5(x²-1/5x+1/100)-39/20`
`=-5[x²-2.x. 1/10+(1/10)^2]-39/20`
`=-5(x-1/10)^2-39/20`
Ta có:`(x-1/10)^2≥0∀x`
`⇒5(x-1/10)^2≥0∀x`
`⇒-5(x-1/10)^2≤0∀x`
`⇒-5(x-1/10)^2-39/20≤-39/20∀x`
Vậy `B_(max)=-39/20` khi `x-1/10=0⇔x=1/10`
`3)C=-2x²-x+1`
`=-(2x²+x-1)`
`=-2(x²+1/2x-1/2)`
`=-2(x²+1/2x+1/16-9/16)`
`=-2(x²+1/2x+1/16)+9/8`
`=-2[x²+2.x. 1/4+(1/4)^2]+9/8`
`=-2(x+1/4)^2+9/8`
Ta có:`(x+1/4)^2≥0∀x`
`⇒2(x+1/4)^2≥0∀x`
`⇒-2(x+1/4)^2≤0∀x`
`⇒-2(x+1/4)^2+9/8≤9/8∀x`
Vậy `C_(max)=9/8` khi `x+1/4=0⇔x=-1/4`
`4)D=-3x²-7x+9`
`=-(3x²+7x-9)`
`=-3(x²+7/3x-3)`
`=-3(x²+7/3x+49/36-157/36)`
`=-3(x²+7/3x+49/36)+157/12`
`=-3[x²+2.x. 7/6+(7/6)^2]+157/12`
`=-3(x+7/6)^2+157/12`
Ta có:`(x+7/6)^2≥0∀x`
`⇒3(x+7/6)^2≥0∀x`
`⇒-3(x+7/6)^2≤0∀x`
`⇒-3(x+7/6)^2+157/12≤157/12∀x`
Vậy `D_(max)=157/12` khi `x+7/6=0⇔x=-7/6`
`5)E=-x²+3x-11`
`=-(x²-3x+11)`
`=-(x²-3x+9/4+35/4)`
`=-(x²-3x+9/4)-35/4`
`=-[x²-2.x. 3/2+(3/2)^2]-35/4`
`=-(x-3/2)^2-35/4`
Ta có:`(x-3/2)^2≥0∀x`
`⇒-(x-3/2)^2≤0∀x`
`⇒-(x-3/2)^2-35/4≤-35/4∀x`
Vậy `E_(max)=-35/4` khi `x-3/2=0⇔x=3/2`
