What is the least possible sum of a positive number and its reciprocal is?

Let this number be x. Then its reciprocal is 1/x. And the sum of them is x+1/x. 

In order to find the least possible sum, we can derivate the sum and set it to zero. 

Derivation of x+1/x gives us, . Setting it to zero, we are going to solve the following equation: 

And solving it, we obtain x=1 and x=-1. Since we were looking for a positive number, the answer is 1