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

x = 1 and y = 10 >1.1 = .9
try others
x = 2 and y =9 > 1/2  1/9
see? 
Using Calculus ....
x+y = 11 > y = 11x
S = 1/x  1/y
= 1/x  1/(11x) = x^1  (11x)^1
dS/dx = 1/x^2  1/(11x)^2
= 0 for a max/min of S
1/(11x)^2 = 1/x^2
x^2 = 11x^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%2811x%29
1/x  1/(11x) becomes infinitely large as x > 0