Answer
Increasing on: $(-\infty, -3), (3, \infty)$
Decreasing on: $(-3,0), (0,3)$
Work Step by Step
$ y=x+\displaystyle \frac{9}{x} \qquad$Discontinuity: $x=0$
$y^{\prime}=1-\displaystyle \frac{9}{x^{2}}$
$=\displaystyle \frac{x^{2}-9}{x^{2}}$
$=\displaystyle \frac{(x-3)(x+3)}{x^{2}}$
$(x-3)(x+3)=0$
Critical numbers: $x=\pm 3$, Discontinuity: $x=0$
$\left[\begin{array}{lllll}
Interval & (-\infty,-3) & (-3,0) & (0,3) & (3,\infty)\\
\text{test point} & -4 & -1 & 1 & 4\\
f^{\prime}(\text{test point}) & 0.4375 & -8 & -8 & 0.4375 \\
\text{sign} & + & - & - & +\\
& \nearrow & \searrow & \searrow & \nearrow
\end{array}\right]$
Increasing on: $(-\infty, -3), (3, \infty)$
Decreasing on: $(-3,0), (0,3)$
