Finding the positive number that minimizes sum with its reciprocal

[rumaithya]

How to find a positive number such that the sum of the number and its reciprocal is as small as possible ?

 

[e(ho0n3]

Let y = x + 1/x. Find the local minimum of y in the first quadrant and you're done. I suggest you also graph y to get a visual.

 

[rumaithya]

thank you.

I was thinking about that before..
In the graph it shows that x = +- 1
but x is +1 when it's local minimum, and x is -1 when it's local maximum.

So the answer would be x = -1

Am I right ?

 

[Galileo]

So the answer would be x = -1
Am I right ?

You were looking for a positive number, right?

 

[rumaithya]

Oh calculus is going to make me feels sick :)

 

[Gokul43201]

Both -1 and +1 are local minima. Ther maxima are at 0 and $$\infty$$