Given: x>0 and xy = 1

We need to find the minimum value of (x + y).

For maximum or minimum value f’(x) = 0.

∴ x = 1 or x =-1

f’’(x) at x = 1.

∴ f’’(x) = 2.

F’’(x)>0 it is decreasing and has minimum value at x = 1

At x = -1

f’’(x) = -2

f’’(x)<0 it is increasing and has maximum value at x = -1.

∴ Substituting x = 1 in f(x) we get

f(x) = 2.

∴ The minimum value of given function is 2.