Consider the scalar differential equation d Define the potential V(x) by Use the chain rule to show that x(t) = f(x). dV (x) dx = -f(x). dv (x(1)) ≤ 0. dt dV (x) dx Let x* be an equilibrium solution of Eq (2). First, show that x* is an extrema of V by calculating (2) -||x=x* = 0. Next, if x* maximizes V, is x* locally stable or unstable? Finally, if x* minimizes V, is x* locally stable or unstable?

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