A particle can move along x-axis under the action of conservative force and its potential energy at any position is given by U=(x2−2x+16)J. Then the particle is in stable equilibrium at

Force acting on the particle, F=−dUdx=(−2x+2)NAt equilibrium, F=0⇒−2x+2=0⇒x=1mNow, d2Udx2=−2. So potential energy is minimum at x = 1m.Hence at x = 1m, the particle is in stable equilibrium.