Question 1143083
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Take the derivative 


    {{{2x}}} - {{{(-2)/x^3}}} = {{{2x}}} + {{{2/x^3}}}.


In the domain x >= 1  the derivative is always positive -- so, the function monotonically grows at x >= 1.


Therefore, the minimum of the function in this domain achieves at x = 1 and is equal to

    {{{1^2}}} - {{{1/1^2}}} = 1 - 1 = 0.



The last step in solving such exercises is to make a plot


    {{{graph( 330, 330, -5, 5, -20, 20,
          x^2 - 1/x^2
)}}}

            Plot y = {{{x^2}}} - {{{1/x^2}}}


to make sure (visually) that our conclusions are correct.
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