a
\({\text{V}}\,\, = \,\,\frac{{{{\text{x}}^{\text{4}}}}}{4}\,\, - \,\frac{{{x^2}}}{2}\,\, \Rightarrow \,\,\frac{{dV}}{{dx}}\,\, = \,\,{x^3}\,\, - \,\,x\,\, = \,\,0\,\, \Rightarrow \,\,x\,\, = \,\,0,\,1,\,\, - \,1\)

\(x\,\, = \,\, \pm 1\,\,\) પાસે \(v \) ન્યૂનતમ છે . 

\({V_{\min }}\, = \,\,{V_{x\,\, = \,\, \pm \,1}}\,\, = \,\,\frac{{{{\left( { \pm \,1} \right)}^4}}}{4}\,\, - \,\,\frac{{{{\left( { \pm \,\,1} \right)}^2}}}{2}\,\, = \,\, - \frac{1}{4}\,\,J\)

આ બિંદુઓ પર ગતિઉર્જા મહતમ છે . 

\(K{E_{\max }}\,\, + \,\,{V_{\min }}\) કુલ યંત્રિકઉર્જા 

\(K{E_{\max }}\,\, - \,\,\frac{1}{4}\, = \,\,2\,\, \Rightarrow \,\,\frac{1}{2}\,\,m{v^2}_{\max }\,\, = \,\,2\,\, + \;\,\frac{1}{4}\,\, = \,\,\frac{9}{4}\)

\( \Rightarrow \,\,\frac{1}{2}\,\, \times \,\,1\,\, \times \,\,{v^2}_{\max }\,\, = \,\,\frac{9}{4}\,\, \Rightarrow \,\,{v_{\max }}\,\, = \,\frac{3}{{\sqrt 2 }}\,\,m/s\)