Let $S=\left\{t \in R: f(x)=|x-\pi| \cdot\left(e^{|x|}-1\right) \sin |x|\right.$ is not differentiable at $\left.t\right\}$. Then the set $S$ is equal to:
$\{0\}$
$\{\pi\}$
$\{0, \pi\}$
$\phi$ (an empty set)
Correct Option: , 4
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