Find a positive number for which the sum of it and its reciprocal is the smallest possible.

We will use the method Minimize f (x) = x + 1/x there for f' (x) = 1 + - 1/x² which can be written as 0 = 1 + - 1/x² which is 1/x² = 1 it makes x² = 1 then x = ±1 We need the positive number so the answer is 1.