Question

The function f(x) = $\left| \frac{x^{2} - 2}{x^{2} - 4} \right|$has

• A. No point of local minima
• B. No point of local maxima
• C. Exactly one point of local minima
• D. ) Exactly one point of local maxima

Answer 1

)

Sol. For y =$\frac { x ^ { 2 } - 2 } { x ^ { 2 } - 4 } , \frac { d y } { d x } = \frac { - 4 x } { \left( x ^ { 2 } - 4 \right) ^ { 2 } }$

⇒ $\frac { d y } { d x }$ > 0 for x < 0 and $\frac { d y } { d x }$ < 0 for x > 0. Then x = 0 is the point of local maxima for y. Now $\left. y \right| _ { x = 0 } = \frac { 1 } { 2 }$ (positive). Thus x = 0 is also the point of local maxima for $y = \left| \frac { x ^ { 2 } - 2 } { x ^ { 2 } - 4 } \right|$