Answer
The answer is below.
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.
