Find a positive number such that the sum of the number and its reciprocal is as small as possible.

Answer 1

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