QUESTION $1$

Let $f$ be a function defined by

$f(x)=x+\frac{1}{x},x0$

$($a$)$ Use the sign pattern for $f^{\text{'}}(x)$ to determine the interval$($s$)$ over which $f$ rises and where it falls.

$(5)$

$($b$)$ Determine the coordinates of the local extreme point$($s$).$

$($c$)$ Use the sign pattern for $f^{\text{'}\text{'}}(x)$ to determine the interval$($s$)$ over which the graph of $f$ is concave up and concave down.