The potential energy of an object is given by U(x)= x⁴ - x²,where U is measured in joules and x is measured in meters.At which position is the object in stable equilibrium? A)only at 0 B)only at 0.707 m C)only at -0.707 m D)at both +0.707 m and -0.707 m E)There isn't a location where the object is in stable equilibrium.

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Quizplus · Accepted Answer

The object is in stable equilibrium where the potential energy is at a minimum. To find the positions where the potential energy is minimized, we take the derivative of the given potential energy expression with respect to x and set it equal to zero: dU/dx = ⁴ - ² = 0 Solving for x, we get x = ±0.707 m. Therefore, the object is in stable equilibrium at both +0.707 m and -0.707 m.

The Potential Energy of an Object Is Given by U(x)=