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X and y are positive integers and x+y=11. What is the largest possible value of 1/x -1/y?

  • Math -

    x = 1 and y = 10 -->1-.1 = .9

    try others
    x = 2 and y =9 --> 1/2 - 1/9
    see?

  • Math -

    Using Calculus ....

    x+y = 11 ---> y = 11-x

    S = 1/x - 1/y
    = 1/x - 1/(11-x) = x^-1 - (11-x)^-1
    dS/dx = -1/x^2 - 1/(11-x)^2
    = 0 for a max/min of S

    -1/(11-x)^2 = 1/x^2
    -x^2 = 11-x^2
    -2x^2 = 11
    x^2 = -11/2
    No real solution , there is no maximum
    see Wolfram
    http://www.wolframalpha.com/input/?i=plot+y+%3D+1%2Fx+-+1%2F%2811-x%29

    1/x - 1/(11-x) becomes infinitely large as x ---> 0

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