c)
$F=4x-x^2+1$
$=-(x^2-4x)+1$
$=-(x-2)^2+5$
$\Rightarrow F\le 5$
Dấu bằng khi $x=2$. $F_{\max}=5$
d)
$G=-x^2-y^2-4y+6x-10$
$=-(x^2-6x)-(y^2+4y)-10$
$=-(x-3)^2+9-(y+2)^2+4-10$
$=-(x-3)^2-(y+2)^2+3$
$\Rightarrow G\le 3$
Dấu bằng khi $x=3,\ y=-2$.
$G_{\max}=3$
a)
$D=-x^2+6x-11$
$=-(x^2-6x+9)-2$
$=-(x-3)^2-2$
$\Rightarrow D\le -2$
Dấu bằng khi $x=3$.
$D_{\max}=-2$
b)
$E=5-8x-x^2$
$=-(x^2+8x)+5$
$=-(x+4)^2+21$
$\Rightarrow E\le 21$
Dấu bằng khi $x=-4$. $E_{\max}=21$
`a) D = -x^2 + 6x - 11`
`= -(x^2 - 6x + 9) - 2`
`= -(x - 3)^2 - 2`
Vì `-(x - 3)^2 <= 0AAx-> -(x - 3)^2 - 2 <= -2AAx`
Dấu "=" xảy ra khi `x = 3`
`b) E = 5 - 8x - x^2`
`= -(x^2 + 8x + 16) + 21`
`= -(x + 4)^2 + 21`
Vì `-(x + 4)^2 <= 0AAx-> -(x + 4)^2 + 21 <= 21AAx`
Dấu "=" xảy ra khi `x = -4`
`c) F = 4x - x^2 + 1`
`= -(x^2 - 4x + 4) + 5`
`= -(x - 2)^2 + 5`
Vì `-(x - 2)^2 <= 0AAx-> -(x - 2)^2 + 5 <= 5AAx`
Dấu "=" xảy ra khi `x = 2`
`d) G = -x^2 - y^2 - 4y + 6x - 10`
`= -(x^2 - 6x + 9) - (y^2 + 4y + 4) + 3`
`= -(x - 3)^2 - (y + 2)^2 + 3`
Vì `{(-(x - 3)^2 <= 0),( -(y + 2)^2 <= 0):}` với `AAx , y`
`-> -(x - 3)^2 - (y + 2)^2 + 3 <= 3AAx , y`
Dấu "=" xảy ra khi `{(x = 3),(y = -2):}`
