A single conservative force \(F_x\) acts on a particle constrained to move along the \(x\)-axis. The graph of \(F_x\) as a function of position \(x\) is shown, where the curve crosses the horizontal axis at \(x = x_1\) and \(x = x_3\), and reaches a local maximum at \(x = x_2\).

Which of the following statements correctly identifies the location of a local minimum in the particle's potential energy \(U(x)\) and provides a valid justification?