Determining Stability from Slope Fields

00:00 3 marks

Consider a differential equation whose slope field shows an equilibrium line at x = 2. The slopes immediately to the left of x = 2 are positive, indicating that solutions increase toward the equilibrium, while the slopes immediately to the right are negative, indicating that solutions decrease toward the equilibrium. Using these slope signs, determine whether the equilibrium at x = 2 is stable or unstable.

Hint Hint

Hint

Recall that if solution trajectories on both sides of an equilibrium approach the equilibrium point, then it is stable.

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Answer Answer

Complete Answer

The equilibrium at x = 2 is stable.

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