The potential energy of a 1 kg mass free to move along the x-axis is given by $V_{(x)}=\bigg[\large\frac{x^4}{4}-\frac{x^2}{2}\bigg]$$J$ The total mechanical energy of the particle is $2J$ then the maximum speed is?

Question

\[(a)\;\frac{3}{\sqrt 2}\; m/s \quad (b)\;\sqrt 2 \;m/s\quad (c)\; \frac{1}{\sqrt 2}\; m/s \quad (d)\;2\; m/s\]