Tìm gtln của F = (4x ^ 2 - 8x + 16)/(x ^ 2 + 4) Giúp với ạ ;(

$\bullet$ Tìm `\text{max}` :

`F=(4x^2 -8x+16)/(x^2 +4)`

`=>F-6=(4x^2 -8x+16)/(x^2 +4)-6`

`=>F-6=(4x^2 -8x+16)/(x^2 +4)-(6(x^2 +4))/(x^2 +4)`

`=>F-6=(4x^2 -8x+16-6x^2 -24)/(x^2 +4)`

`=>F-6=(-2x^2 -8x-8)/(x^2 +4)`

`=>F-6=(-2(x^2 +4x+4))/(x^2 +4)`

`=>F-6=(-2(x+2)^2)/(x^2 +4)<=0AAx`

`=>F<=6`

Dấu "=" xảy ra `<=>x+2=0<=>x=-2`

Vậy `\text{max}_F =6<=>x=-2` 

$\bullet$ Tìm `\text{min}` :

`F=(4x^2 -8x+16)/(x^2 +4)`

`=>F-2=(4x^2 -8x+16)/(x^2 +4)-2`

`=>F-2=(4x^2 -8x+16)/(x^2 +4)-(2(x^2 +4))/(x^2 +4)`

`=>F-2=(4x^2 -8x+16-2x^2 -8)/(x^2 +4)`

`=>F-2=(2x^2 -8x+8)/(x^2 +4)`

`=>F-2=(2(x^2 -4x+4))/(x^2 +4)`

`=>F-2=(2(x-2)^2)/(x^2 +4)>=0AAx`

`=>F>=2`

Dấu "=" xảy ra `<=>x-2=0<=>x=2`

Vậy `\text{min}_F =2<=>x=2`