(1) Find the absolute extrema of on the interval  .

First, we find the critical numbers





  
  
  
  
  
  
  
  
  
  
  
  

  
There is only one critical number x = 2 in the interval.

        2
-----+-------
+ +  | - - - -

As you can see, ther e is a relative maximum at x = 2, so this is also an absolute maximum (because there is only one critical number in the interval).

CONCLUSION:

is the ABSOLUTE MAXIMUM, and it occurs at x = 2.
There is NO ABSOLUTE MINIMUM.