Let $f(x)=x \sin(x)$. Then $|f|$ is?

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Let $f(x)=x \sin(x)$. Then $|f|$ is ?

  1. Differentiable at $x=\pi$
  2. Differentiable at $x=0$
  3. Uniformily continious on $\mathbb{R}$
  4. Differentiable at $x=-\pi$

I think only 3 is correct. but how to prove it?

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