Find the positive numbers such that the sum of and its reciprocal is as small as possible. Does this problem require optimization over an open interval or a closed interval

Yes and closed interval

Step-by-step explanation:

The computation is shown below:

For the sum and the reciprocal as small as the possible equation is as follows

Now take out the derivates,

So,

or we can say that

As the only positive number is to be determined i.e

x = 1

So this problem needed the optimization over a closed interval and the same is to be considered.

24

step-by-step explanation: