The Mathematica code

```
f := #1 + Sin[2 #1] &;
inflectionPoints = Table[{x, f[x]}, {x, -Pi, Pi, Pi/2}];
stationaryPoints = Union[
   Table[{x, f[x]}, {x, -2 Pi/3, Pi/3, Pi}], 
   Table[{x, f[x]}, {x, -Pi/3, 2 Pi/3, Pi}]];
Show[Plot[f[x], {x, -Pi - 1, Pi + 1}], 
     ListPlot[{stationaryPoints, inflectionPoints}, 
     PlotStyle -> {{Red}, {Blue}}, 
  PlotMarkers -> {Automatic, 15}]]

```

produces:

![original](https://i.stack.imgur.com/DRJYf.png)

The points (circles and squares) are supposed to be at the critical points, but (as can be seen most clearly via the point at the origin) the points are too far down and too far left.

After manually adjusting the points, I expect the original output should look more like this:
![enter image description here](https://i.stack.imgur.com/l3KVV.png)

Question
========

Why are the points being rendered at the wrong positions? How can this be fixed?

(First) Response to answers
===========================

First off, yoda suggested that this might be OS dependent. I am using Ubuntu 9.10 32-bit with Mathematica 8.0.1.0.

Mr. Wizard's code looks correct in my Mathematica, but if I remove the frame, then the points are rendered too far to the left:

![enter image description here](https://i.stack.imgur.com/ErNOA.png)

belisarius's code from his machine looks good (see picture in his answer), but on my Mathematica, the points are again rendered too far to the left:

![enter image description here](https://i.stack.imgur.com/uqfzt.png)

Mr. Wizard and belisarius (and others), do these new facts change your answer?

Conclusion
==========

I believe Mr. Wizard's (as explained in more detail by Alexey Popkov) provides the correct answer. My example (above) of Mr. Wizard's code having points slightly shifted to the left seems to be a different problem. Namely, the picture is so small that Mathematica cannot position things properly. Using a larger image size, everything appears to be in the correct position.