The function f ( x ) = x x 2 - 6 x - 16 , x ? R - { - 2 , 8 } [2024] Differential Calculus jee mains questions

Question

The function $f (x) = \frac{x}{x^{2} - 6 x - 16}, x \in R - {- 2, 8}$ [2024]

Smart Achievers · Accepted Answer

(4)

$f (x) = \frac{x}{x^{2} - 6 x - 16}$

$\Rightarrow f' (x) = \frac{(x^{2} - 6 x - 16) (1) - x (2 x - 6)}{{(x^{2} - 6 x - 16)}^{2}}$

$= \frac{- x^{2} - 16}{{(x^{2} - 6 x - 16)}^{2}} < 0 \forall x$

$∴ f (x) is a decreasing function in its domain.$

$\Rightarrow f (x) decreases in (- \infty, - 2) \cup (- 2, 8) \cup (8, \infty)$

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