Asked by Soojung
Find a positive number such that the sum of the number and its reciprocal is as small as possible.
Answers
Answered by
Reiny
let the number be x
and the sum as described be S
S = x + 1/x
dS/dx = 1 - 1/x^2
= 0 for a max/min of S
1 = 1/x^2
x = ±1 , but x had to be positive
if x=1, then S = 1+1/1 = 2
test: let x = 1.01, S = 1.01 + 1/1.01 > 2
let x= .99, then S = .99 + 1/.99 = 2.000101 > 2
so the number is 1
and the sum as described be S
S = x + 1/x
dS/dx = 1 - 1/x^2
= 0 for a max/min of S
1 = 1/x^2
x = ±1 , but x had to be positive
if x=1, then S = 1+1/1 = 2
test: let x = 1.01, S = 1.01 + 1/1.01 > 2
let x= .99, then S = .99 + 1/.99 = 2.000101 > 2
so the number is 1
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.