Question

tìm GTLN 

x+1-x^2 

Answer 1

`A=x+1-x^2`

`A=-(x^2-x-1)`

`A=-(x^2-x+1/4-5/4)`

`A=(x^2-x+1/4)+5/4`

`A=5/4-(x-1/2)^2 <= 5/4`

dấu ''`=`'' xảy ra khi`x-1/2=0=>x=1/2`

vậy `MaxA=5/4<=>x=1/2`

Answer 2

\(x+1-x^2=-\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{5}{4}=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{5}{4}\le\dfrac{5}{4}\forall x\)

Dấu "=" xảy ra <=> \(x=\dfrac{1}{2}\)