# Math Help - positive number, sum of it and recip. small as possible

1. ## positive number, sum of it and recip. small as possible

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

??

2. Originally Posted by rsanford
"Find a positive number such that the sum of the number and its reciprocal is as small as possible."

??
$S = x + \frac{1}{x}$.

Find the minimum using calculus:

$\frac{dS}{dx} = 1 - \frac{1}{x^2}$.

Stationary points: Solve $0 = 1 - \frac{1}{x^2}$ subject to the restriction x > 0.

I get $x = 1$. Test nature ....

The minimum value occurs at x = 1 and the minimum value is S = 2.

3. thank you!