Answer:
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
[tex]\(\frac{d}{dx}\left(x+\frac{1}{x}\right)=0.\)[/tex]
Now take out the derivates,
So,
[tex]\(1-\frac{1}{x^2}=0,\)[/tex]
or we can say that
[tex]\(x^2-1=0\rightarrow x=\pm1.\)[/tex]
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.
