# Second derivative at the point of stable equilibrium

To insure a point of stable equilibrium, the necessary and sufficient conditions on the potential energy of a physical system, U = U(x), are that dU/dx = 0. What does the second derivative at that point have to be?

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For the equilibrium to be stable the point must be a minima of the potential energy.

A minima point means that the second derivative is POSITIVE.

Think about it as a valley or a dip in the potential energy curve. The force is ...

#### Solution Summary

The solution explains what the sign of the second derivative should be for a system to be in a stable equilibrium

$2.19