Question

For f(x) = x + `1/x` (x ≠ 0)

Options

• local maximum value is 2

• local minimum value is –2

• local maximum value is –2

• local minimum value < local maximum value

Answer 1

local maximum value is –2

Explanation:

f'(x) = 1 – `1/x^2`

f'(x) = 0

1 = `1/x^2` 

⇒ x² = 1

⇒ x = ±1

At x = 1, f(1) = 2 (Local minimum for x > 0)

At x = –1, f(–1) = –2 (Local maximum for x < 0).