Find a positive number such that the sum of the number and its reciprocal is as small as possible.
Let the positive number be x. So we have x > 0
we want x + 1/x to be a minimum.
let y = x + 1/x
=> y' = 1 - 1/x^2
for min, set y' = 0
=> 1 - 1/x^2 = 0
=> 1/x^2 = 1
=> x^2 = 1
=> x = +/- 1
=> x = 1, since x > 0
you can check +1 and -1 using the second derivative test if you want to be sure of this, or graph x + 1/x