The behavior of FindMinimum depends on the Method and on values of its sub-options.
Please post the code you used to produce the graphics.

Here's the code:

Thanks for pointing that out Alexey.  I have looked at the Unconstrained Optimization tutorial, but didn't go to the one on Newton's method.  Personally, I think that the Options function in Mathematica should be made more powerful so you can somehow see Options on Options.  Perhaps some sort of tree structure.

Frank,
I cannot find in the Documentation any mention of the "StepControl" suboption for the "InteriorPoint" method. Please provide a link if you have.
Brief search give me only this: The Method Options of "InteriorPoint".

Frank,
Yes, unfortunately the absence of an error message does not necessarily mean that the option is available. Only presence of an error message should be considered as a prove that the option is not supported, but even for this rule may be rare exceptions. The official politics of the WRI is that only documented behavior is supported. At the same time, the Documentation is very sparse and it sometimes takes hours even for an experienced user to find an "obvious" option hidden deeply in the Documentation. This thread is an illustration: how much time you would spend finding all that information having only the Documentation? I am certain that a newbie has no chance! Note also how simple and obvious looks the answer: it is hard to believe that such "obvious" things are really deeply hidden and in practice are unavailable even for experienced users...