JEE Mains · Maths · STD 12 - 6. Application of derivatives
Consider the function \(f : R \rightarrow R\) defined by \(f(x)=\left\{\begin{array}{cc}\left(2-\sin \left(\frac{1}{x}\right)\right)|x|, x \neq 0 \\ 0 & , x=0\end{array} .\right.\) Then \(f\) is
- A monotonic on \((-\infty, 0) \cup(0, \infty)\)
- B not monotonic on \((-\infty, 0)\) and \((0, \infty)\)
- C monotonic on \((0, \infty)\) only
- D monotonic on \((-\infty, 0)\) only
Answer & Solution
Correct Answer
(B) not monotonic on \((-\infty, 0)\) and \((0, \infty)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cl}-x\left(2-\sin \left(\frac{1}{x}\right)\right) & x<0 \\ 0 & x=0 \\ x\left(2-\sin \left(\frac{1}{x}\right)\right) & \end{array}\right.\)…
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