Minimum Value | MCQs

Explanation

Given xy = 1 and x > 0:

y = 1/x

We want to minimize x + y = x + 1/x.

Let's find the minimum value:

Let f(x) = x + 1/x

f'(x) = 1 - 1/x² = 0 for minimum

x² = 1

x = 1 (since x > 0)

f(1) = 1 + 1/1 = 2

The minimum value of x + y is 2.