This turned out to be a popular problem and we had lots of correct solutions - well done to everybody.
Emily and Kaia from Stoke-By-Nayland School and Josh from Maungatapere School were first in with well-explained answers.

The person was moving quickest at the point where the graph's slope or gradient, either up or down, is steepest.

Between 9 seconds and 12 seconds they walked 4 metres, so a reasonable estimate for the speed can be found dividing the distance by the time.

4 metres in 3 seconds gives an average of around 1.3 m/s

Average speeds for other parts of the motion can be estimated in a similar way to give approximate speeds of 0.6 m/s, 0.5 m/s, then the 1.3 m/s (fastest) and finally 0.25 m/s

Nearly everyone went on to give the lowest speed as the final part of the motion - that's around 0.25 m/s . But see what Alice from Montreal thinks :

The lowest speed must be zero.

If the person switches direction, say they were going forwards and then go backwards, or the other way round, then there was an instant when they stopped.

Even if it was almost no time at all there was still a point in the motion when the speed, just for that moment, must have been zero.

In this question that happened three times :

At around 9 seconds, 12 seconds and 16 seconds, the person switched between motion forwards and motion backwards.

That's pretty good thinking, Alice!