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.