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Problem $1$

Consider the function $f(x)=1\frac{1}{x}\frac{1}{\frac{}{(E{)}^2}}.$

$($a$)$ Find the asymptotes of $f.$

$($b$)$ Find the intervals for which $f$ is increasing and for which it is decreasing.

$($c$)$ Find the intervals for which $f$ is concave upward and for which it is concave downward.