Question

f(x) = x + $\frac{1}{x}$, x ≠ 0 then

• A. f(x) has no point of local maxima
• B. f(x) has no point of local minima
• C. f(x) has exactly one point of local minima
• D. f(x) has exactly two points of local minima

Answer 1

Answer: (C)

f(x) has exactly one point of local minima

Answer 2

f (x) = $1 - \frac { 1 } { x ^ { 2 } } = \frac { ( x - 1 ) ( x + 1 ) } { x ^ { 2 } }$. If x > 1

⇒ f '(x) > 0 for x > 1 or x < −1, and f '(x) < 0 for x ∈ (-1, 1) ~ {0}. Thus x = 1 is the point of local minima and x = −1 is the point of local maxima.