A transverse wave travels along rope .the graph shows the variation of the displacement of particles in the rope with distance along it at a particular instant .at which distance along the rope do particles have max upwards velocity

Since the wave is moving to the right, we can draw the position of the wave at the next instant by simply replicating the wave, but shifted to the right.

In this way, we can know how each point has moved in the next instant. It can be seen that particles at both 0.5 m and 1.0 m will move upward at the next instant but the largest upward change in displacement occurs at a distance of 0.5 m.

At 1.5 m and 2.0 m, the particles would move downward in the next instant, and the maximum downward velocity is at 1.5 m.