MCQ
Let a function $f\left( x \right) = \left\{ \begin{gathered}
   - \ln \left( {3x - \left[ {3x} \right]} \right)\,;\,\,3x \ne n;n \in N \hfill \\
  \ln \left( {\operatorname{sgn} \left( {3x} \right)} \right)\,\,\,\,\,\,\,;\,\,3x = n;n \in N \hfill \\ 
\end{gathered}  \right.,$ (where [.] and sgn $(x)$ denotes greatest integer function and signum function respectively) then number of point $(s)$ , where $f(x)$ is minimum in $x  \in  (0, 5)$ , is 
  • A
    $0$
  • B
    $4$
  • C
    $5$
  • $14$

Answer

Correct option: D.
$14$
d
$f(\mathrm{x})=\left\{\begin{array}{ll}{-\ln \{3 \mathrm{x}\}} & {; 3 \mathrm{x} \neq \mathrm{n}} \\ {0} & {; 3 \mathrm{x}=\mathrm{n}}\end{array}\right.$

Graph of $f(\mathrm{x})$ will be

$\therefore \quad$ Local minima at $\mathrm{x}=\frac{1}{9}, \frac{2}{3}, \frac{3}{3}, \ldots \ldots, \frac{14}{3}$

$\Rightarrow 14$ points.

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