SOLUTION: Determine the location and value of the absolute extreme values of f on the given interval, if they exist. f(x)=12x^(2/3) -x on [0,1728]

Question 1155624: Determine the location and value of the absolute extreme values of f on the given
interval, if they exist. f(x)=12x^(2/3) -x on [0,1728]
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Determine the location and value of the absolute extreme values of f on the given
interval, if they exist. f(x)=12x^(2/3) -x on [0,1728]

 on [0,1728] 



To find potential extrema set f'(x) = 0 



2nd derivative test for max or min







That's negative so relative maximum at x=512.

We find the value there.



So relative maximum is (512,256)

We must examine to see if endpoints of interval are higher points.




Thus absolute maximum at (512,256), absolute minima at (0,0) and (1728,0)

Edwin

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