Question

Total number of critical points of f(x) = $\left| \frac{2 - x}{x^{2}} \right|$are equal to

• A. 3
• B. 2
• C. 1
• D. 4

Answer 1

Answer: (B)

2

Answer 2

f(x) = $\left\{ \begin{array} { l l } \frac { 2 - x } { x ^ { 2 } } , & x < 2 \\ \frac { x - 2 } { x ^ { 2 } } , & x \geq 2 \end{array} \right.$

⇒ f(x) =

f '(2 − 0) = − $\frac { 1 } { 4 }$ , f '(2 + 0) = $\frac { 1 } { 4 }$.

Thus f(x) is non diff. at x = 2. If f (x) = 0

⇒ $\frac { 4 } { x ^ { 3 } } = \frac { 1 } { x ^ { 2 } }$ ⇒ x = 4.

Thus there are two critical points namely x = 2, 4.

(Note that x = 0 is not the critical point as x = 0 is not in the domain).