Let f:mathbb Rtomathbb R be defined by f(x)=begincasesx^4(2+sindfrac1x), & xne0, 0, & x=0.endcases Then which of the following statement(s) is (are) true?

Q34Section B (Section B)34 of 60

Extremum, monotonicity and differentiability at zero

Let $f:\mathbb R\to\mathbb R$ be defined by

$f(x)=\begin{cases}x^4\left(2+\sin\dfrac1x\right), & x\ne0,\ 0, & x=0.\end{cases}$

Then which of the following statement(s) is (are) true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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