Ta có :
\(N=x-x^2=-x^2+x-\dfrac{1}{4}+\dfrac{1}{4}=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\)
Do : \(\left(x-\dfrac{1}{2}\right)^2\ge0\Rightarrow-\left(x-\dfrac{1}{2}\right)^2\le0\Rightarrow-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}\le\dfrac{1}{4}\)
Vậy GTLN của N là \(\dfrac{1}{4}\) . Dấu \("="\) xảy ra khi \(x-\dfrac{1}{2}=0\Leftrightarrow x=\dfrac{1}{2}\)