Function f(x) = | x - 1 | x^2 is monotonic decreasing in- - Vidyadip

MCQ

Function $f(x) = \frac{{\left| {x - 1} \right|}}{{{x^2}}}$ is monotonic decreasing in$-$

A
$( - \infty ,\infty )$
B
$(0,1)$
C
$(2. \infty)$
D
$(0,1) \cup (2,\infty )$

✓

Answer

$f(x)=\left\{\begin{array}{ll}{-\frac{(x-1)}{x^{2}}} & {; x \in(-\infty, 0) \cup(0,1)} \\ {\frac{(x-1)}{x^{2}}} & {; x \in(1, \infty)}\end{array}\right.$
$f(x)=\left\{\begin{array}{l}{\frac{x(x-2)}{x^{4}} ; x \in(-\infty, 0) \cup(0,1)} \\ {\frac{-x(x-2)}{x^{4}} ; x \in(1, \infty)}\end{array}\right.$

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