## Essential University Physics: Volume 1 (3rd Edition)

We take the derivative and set it equal to zero to find equilibria: $\frac{dU}{dx}=6x^2-4x-7 \ \ 0=6x^2-4x-7 \\ x=-.8,1.46$ We take the second derivative to find: $\frac{d^2U}{dx^2}=12x-4$ We plug in the equilibria. $x=-.8$ yields a negative value, so it is an unstable equilibrium. $x=1.46$ yields a positive value, so this equilibrium is stable.