Asked by Shohanur
X and y are positive integers and x+y=11. What is the largest possible value of 1/x -1/y?
Answers
Answered by
Damon
x = 1 and y = 10 -->1-.1 = .9
try others
x = 2 and y =9 --> 1/2 - 1/9
see?
try others
x = 2 and y =9 --> 1/2 - 1/9
see?
Answered by
Reiny
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.