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

A potential energy function $U(x)$ always implies a conservative force, so option A is correct. The force is given by $F(x)=-dU/dx=-(2ax-b)=-2ax+b$, so option D is correct. For equilibrium, $F(x)=0$, which means $-2ax+b=0$, so $x=b/(2a)$. Thus, option B is correct. To check stability, we find the second derivative of potential energy: $d^{2}U/d{x}^2=2a$. Since $a$ is positive, $d^{2}U/d{x}^2>0$ at the equilibrium position, indicating stable equilibrium. So, option C is correct.