Answer
(a) At points b and d, the force on the marble is zero.
(b) Point b is a position of stable equilibrium.
(c) Point d is a position of unstable equilibrium.
Work Step by Step
(a) $F = -\frac{dU}{dx} = 0$
The force on the marble is zero when the slope of the potential energy curve is zero.
At points b and d, the force on the marble is zero.
(b) Stable equilibrium points are minima in the potential energy curve. Therefore, point b is a position of stable equilibrium.
(c) Unstable equilibrium points are maxima in the potential energy curve. Therefore, point d is a position of unstable equilibrium.
