Let $f(x)=\frac{2x+8}{x^4}.$ In the following questions, you may use the facts that

$f^{\text{'}}(x)=-\frac{6x+32}{x^5},$ and $,f^{\text{'}\text{'}}(x)=\frac{24x+160}{x^6}$

Make sure to show all your work.

$($a$)(7$ points$)$ On which intervals is $f(x)$ increasing? On which intervals is it decreasing?

$($b$)(7$ points$)$ On which intervals is $f(x)$ concave up$?$ On which intervals is it concave down?

$($c$)(7$ points$)$ Find the $x-$coordinates of any critical points of $f(x)$ and classify each one as the location of a local maximum, local minimum, or neither one.

$($d$)(4$ points$)$ Find the $x-$coordinates of any points of inflection on the graph of ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x).$ If there are no inflection points, then explain why.