Question 9: Find the maximum of the function (y = – frac{1}{4}{x^4} + 2{x^2} – 1)

\(y’ = – {x^3} + 4x, y” = – 3{x^2} + 4\)

\(y’ = 0 \Leftrightarrow \left[\begin{array}{l}x=0\Rightarrowy”\left(0\right)=4>0\\x=\pm2\Rightarrowy”\left({\pm2}\right)=–8<0\end{array}\right\)[\begin{array}{l}x=0\Rightarrowy”\left(0\right)=4>0\x=\pm2\Rightarrowy”\left({\pm2}\right)=–8<0\end{array}\right\)

So the function peaks at \(x = \pm 2\)