# Math

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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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