a, Đặt \(t=x^2\) trên \(\left[0;4\right]\)
\(y=g\left(t\right)=t^2-2t\)
\(g\left(0\right)=0;g\left(4\right)=8;g\left(1\right)=-1\)
\(\Rightarrow Maxy=8\Leftrightarrow t=4\Leftrightarrow x=-2\)
\(Miny=-1\Leftrightarrow t=1\Leftrightarrow x=\pm1\)
b, \(y=\left(x^2+x\right)-\left(x^2+x\right)\)
Đặt \(t=x^2+x\) trên \(\left[0;2\right]\)
\(y=g\left(t\right)=t^2-t\)
\(g\left(0\right)=0;g\left(2\right)=2;g\left(\frac{1}{2}\right)=-\frac{1}{4}\)
\(\Rightarrow Maxy=2\Leftrightarrow t=2\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
\(Miny=-\frac{1}{4}\Leftrightarrow t=\frac{1}{2}\Leftrightarrow x=\frac{-1\pm\sqrt{3}}{2}\)
