If f(x) = x + 1/x for x > 0, the minimum value of f(x) is:

Model Answer & Options

Source: Extra Practice

0

1

2

None of these

Explanation

f'(x) = 1 - 1/x². Setting f'(x) = 0 gives 1 = 1/x², so x² = 1. Since x > 0, we take x = 1. f''(x) = 2/x³, so f''(1) = 2 (positive), which confirms a minimum at x=1. The minimum value is f(1) = 1 + 1/1 = 2. This can also be solved using the AM-GM inequality: (x + 1/x)/2 ≥ √(x * 1/x) => x + 1/x ≥ 2.

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