The particle has the greatest kinetic energy at x=3.
Work Step by Step
From x=0 to x=3, the particle is being pushed forward by a force in the positive direction. The particle accelerates during that whole period because only one force is acting upon it. At x=3, the particle is traveling at its fastest speed, therefore it has the greatest kinetic energy. Once it reaches x=3, the force becomes negative and slows down the particle, consequently decreasing kinetic energy.