# Chapter 12 - Exercises and Problems - Page 222: 21

#### Work Step by Step

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.

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