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6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
Function $f(x) = \frac{{\left| {x - 1} \right|}}{{{x^2}}}$ is monotonic decreasing in-
  • A
    $( - \infty ,\infty )$
  • B
    $(0,1)$
  • C
    $(2. \infty)$
  • ✓
    $(0,1) \cup (2,\infty )$
✓

Answer

Correct option: D.
$(0,1) \cup (2,\infty )$
d
$f(x)=\left\{\begin{array}{ll}{-\frac{(x-1)}{x^{2}}} & {; x \in(-\infty, 0) \cup(0,1)} \\ {\frac{(x-1)}{x^{2}}} & {; \quad x \in(1, \infty)}\end{array}\right.$

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

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