Question: Problem 6.

“Graph” the function \[f(x)=\frac{{{x}^{2}}+2}{x}\]. Use the fact that

\[\begin{aligned} & {f}'(x)=\frac{{{x}^{2}}-2}{{{x}^{2}}} \\ & \\ \end{aligned}\] \[\begin{aligned} & {f}''(x)=\frac{4}{{{x}^{3}}} \\ & \\
\end{aligned}\]
Find:

(a) Domain.

(b) x- and y-intercepts.

(c) Horizontal asymptotes, if any.

(d) Vertical asymptotes, if any.

(e) Critical numbers, intervals when the function is increasing and decreasing.

(f) Inflection points, concavity.