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Use the theorem on the Stability of Equilibrium Points to determine the stability of the equilibrium points O and 1 and how they depend

 

Use the theorem on the Stability of Equilibrium Points to determine the stability of the equilibrium points O and 1 and how they depend on r. Determine the stability of the equilibrium point x = 0 and how the stability depends on r. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The equilibrium point 0 is unstable for all r. B. The equilibrium point 0 is stable for 0 C. The equilibrium point 0 is unstable for D. The equilibrium point 0 is unstable for 0 E. The equilibrium point 0 is stable for O F. The equilibrium point 0 is stable for all r.

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