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The function $f : \mathbb{R}\rightarrow \mathbb{R}$ is defined by

$$f(x)= \left\{\begin{matrix}
e^{-\frac{1}{x}}, & x > 0\\ 
 0,& x \leq 0\;.
\end{matrix}\right.$$

Then

  1. $f$ is not continuous

  2. $f$ is continuous, but not differentiable everywhere

  3. $f$ is differentiable but $f’$ is not continuous

  4. $f$ is differentiable and $f’$ is continuous

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