A function \(f : \mathbb{R} \rightarrow \mathbb{R}\) is defined by

\(f(x) = e^{-\frac{1}{x}}\) for \(x>0\), and \(0\) for \(x \leq 0\).

Then is \(f\) continuous and differentiable? Is \(f'\) continuous?

A function \(f : \mathbb{R} \rightarrow \mathbb{R}\) is defined by

\(f(x) = e^{-\frac{1}{x}}\) for \(x>0\), and \(0\) for \(x \leq 0\).

Then is \(f\) continuous and differentiable? Is \(f'\) continuous?

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