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Application of Derivatives question

2021 · 17 Mar · Shift 2 · Q30

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PYQ Library
JEE Main
Mathematics
Application of Derivatives
2021 · 17 Mar · Shift 2 · Q30

Application of Derivatives question

2021 · 17 Mar · Shift 2 · Q30

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

Consider the function

f : \mathbb{R} \to \mathbb{R}

defined by

f(x) = \left\{ \begin{array}{ll} \left(2 - \sin\left(\dfrac{1}{x}\right)\right)|x| & x \ne 0 \\ 0 & x = 0 \end{array} \right.

Then

f

is :

A
not monotonic on ( $-\infty$ , 0) and (0, $\infty$ )
B
monotonic on (0, $\infty$ ) only
C
monotonic on ( $-\infty$ , 0) only
D
monotonic on ( $-\infty$ , 0) $\cup$ (0, $\infty$ )

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