Consider the function $f:R \to R$ defined by $f(x) = \left\{ {\begin{array}{*{20}{c}} {\left( {2 - \sin \left( {\frac{1}{x}} \right)} \right)|x|,}&{x \ne 0}\\ 0&{,x \ne 0} \end{array}} \right\}$. Then $f$ is

monotonic on $(0,\,\infty )$ only

monotonic on $( - \infty ,\,0)$ only

JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

Consider the function

f:R \to R

defined by

f(x) = \left\{ {\begin{array}{cccccccccccccccccccc} {\left( {2 - \sin \left( {\frac{1}{x}} \right)} \right)|x|,}&{x \ne 0}\\ 0&{,x \ne 0} \end{array}} \right\}

. Then

f

View answer and explanation

Correct option: B

not monotonic on

( - \infty ,\,0) \cup (0,\,\infty )

Option B is correct. The function f(x) is not monotonic on

( - \infty ,\,0) \cup (0,\,\infty )

because its derivative oscillates.