A first order nonlinear system is described by the equation ẋ = −f(x) where f(x) is a continuous and differentiable nonlinear function that satisfies the following: f(0) = 0; f(x) > 0 for x > 0; f(x) < 0 for x < 0. Use the Lyapunov function V(x) = x2 /2 to show that the system is stable near the origin.

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