First solve the equation f(x) = 0 to find the critical points of the given autonomous differential equation dr/dt = f(r). Then analyze the sign of f(x) to determine whether each critical point is stable or unstable, and construct the corresponding phase diagram for the differential equation. (a) 3x - x². dz dt (b) dt = (x - 2)² [From Wikipedia "if one arrow points towards the critical point, and one points away it is semi-stable (a node): it is stable in one direction (where the arrow points towards the point), and unstable in the other direction (where the arrow points away from the point)."] dz = 7x-²-10. = (²+1)(²-1)

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