Please explain this maxima minima problem.

Dear student 
For this function, f'(x)= 1, if x>2 
                                  =-1 if x<2 ,which can be expressed as x-2|x-2|so f'(x) is not zero at any point , so only points which are to be considered for maxima and minima are the points of non differentiability, i.e2, and the end point of domain, i.e -2 and 5 ,  
so the values ath these three points has been considered and compared. rest you might have understood 
With regards 

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