The potential energy of a particle is U(x) = ax⁴ - bx², where a>0 and b>0. Which statement is correct?
Options

Question

The potential energy of a particle is U(x) = ax⁴ − bx², where a>0 and b>0. Which statement is correct?

G1 Physics · Accepted Answer

dU/dx = 4ax³ − 2bx = 2x(2ax²−b). Equilibria occur at x=0 and x=±√(b/2a). At x=0, d²U/dx²=−2b<0, so it is unstable. The other two are stable.