Question 1135313
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1.  They ask you to find the minimum of the function

        f(x) = x + {{{1/x}}}

    in the interval  I = [1/2, 3].



    Take the derivative, equate it to zero and find the root:


    f'(x) = 1 - {{{1/x^2}}};   f'(x) = 0  is the equation  1 - {{{1/x^2}}} = 0;

    as an equation, it is equivalent to  {{{x^2}}} = 1,  which has only one root  x= 1  in the given interval.



    <U>ANSWER</U>.  x = 1.



To better illustrate the situation for you, I placed the plot below:



    {{{graph( 330, 330, -1.5, 3.5, -5.5, 5.5,
          x + 1/x
)}}}


        Plot y = x + {{{1/x}}}.
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