અહી, \(U( x )=\frac{ x ^{4}}{4}-\frac{ x ^{2}}{2}\)

\(\therefore \frac{ dV }{ dx }=\frac{4 x ^{3}}{4}-\frac{2 x }{2}= x ^{3}- x\)

જ્યારે \(U\) લઘુતમ થાય ત્યારે \(\frac{ dV }{ dx }=0\)

\(\therefore x ^{3}- x =0\)

\(\therefore x \left( x ^{2}-1\right)=0\)

\(\therefore x =0, \pm 1\)

\(U_{\min }(x=\pm 1)=\frac{1}{4}-\frac{1}{2}=-\frac{1}{4} J\)

\(K . E_{\max }=2-\left(-\frac{1}{4}\right)=\frac{9}{4} J =\frac{1}{2} mv _{\max }^{2}\)

\(\therefore v _{\max }^{2}=\frac{2 \times 9}{4}=\frac{9}{2}\)

\(\therefore v _{\max }=\frac{3}{\sqrt{2}} m / s\)