The function f(x)=x x^2-6 x-16 , x R - -2,8 - Vidyadip

MCQ

The function $f(x)=\frac{x}{x^2-6 x-16}, x \in R -\{-2,8\}$

A
decreases in $(-2,8)$ and increases in $(-\infty,-2) \cup(8, \infty)$
B
decreases in $(-\infty,-2) \cup(-2,8) \cup(8, \infty)$
C
decreases in $(-\infty,-2)$ and increases in $(8, \infty)$
D
increases in $(-\infty,-2) \cup(-2,8) \cup(8, \infty)$

✓

Answer

$f(x)=\frac{x}{x^2-6 x-16}$
Now,
$f^{\prime}(x)=\frac{-\left(x^2+16\right)}{\left(x^2-6 x-16\right)^2}$
$f^{\prime}(x)<0$
Thus $f(x)$ is decreasing in
$(-\infty,-2) \cup(-2,8) \cup(8, \infty)$

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