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On-linear system by approximating the system, near equilibrium points, by linear systems. Part 1: As a warm up, let's review the case of a single, first order differential equation of the form y' f(y). Let the point y0 be an equilbrium point. Below are two examples of functions f and equilibrium points y0. For each of the examples, draw the phase line and classify the type of equilibrium. Note the relationship between the sign of the derivative f'(y0) and the type of equilibrium. Then fill in.

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