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Question: How to get CriticalPoints to return only valid critical points

I'm trying to use the CriticalPoints command from the Student[Calculus1] package to determine the critical points of f(x) = x^2 * ln(x).

 

with(Student[Calculus1]):

f := proc (x) options operator, arrow; x^2*ln(x) end proc:

`assuming`([CriticalPoints(f(x))], [x > 0])

[0, exp(-1/2)]

(1)

``

My issue is this. A critical point is defined as a value of x in the domain of f(x) where either f'(x)=0 or f'(x) does not exist. Clearly x=0 is not in the domain of f(x) = x^2*ln(x). How may I "trick" Maple into returning only the value exp(-1/2)?  As seen above, my attempt to use the assuming command proved futile.

More troubling, however, is whether or not the CriticalPoints command is using the correct definition to compute critical points. Can anyone shed some light on this?

 

Download critpts.mw

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