Physics - W.E.P. Question with Solution | TestHub

$\mathrm{U}=2{\mathrm{x}}^4-27\mathrm{x}$

$\frac{\mathrm{dU}}{\mathrm{dx}}=8{\mathrm{x}}^3-27$

At$\mathrm{x}=\frac{3}{2},\frac{\mathrm{dU}}{\mathrm{dx}}=0$, therefore it is an equilibrium position.

$\frac{{\mathrm{d}}^2\mathrm{U}}{{\mathrm{dx}}^2}=24{\mathrm{x}}^2$

At$\mathrm{x}=\frac{3}{2},\frac{{\mathrm{d}}^2\mathrm{U}}{{\mathrm{dx}}^2}>0$, therefore it is a stable equilibrium position.