What is the smallest sum that can be obtained by adding a positive number?

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  • November 23, 2017 at 10:51 am #16198
    kingsly
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    What is the smallest sum that can be obtained by adding a positive number and its reciprocal?

    November 23, 2017 at 10:52 am #16199
    kingsly
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    Answer

    Let the number be x and its reciprocal is 1/x
    We need to find the minimum value of the sum of x and 1/x
    So Min (x + 1/x)
    By the first order condition we have
    d(x+1/x)/dx = 0
    which means 1+ (-1)x^-2 = 0
    solving for x we get x = +1 (since x can be only positive)
    now if x is + 1 then minimum sum is 1 + 1 = 2

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