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The greatest integer function $$f ( x ) = \lfloor x \rfloor$$ , defined for all values of $$x$$ , assumes a local maximum value of $$0$$ at each point of $$[ 0,1 )$$ . Could any of these local maximum values also be local minimum values of $$f$$ ? Give reasons for your answer.
$$\text { Yes, except at } x = 0$$