The function f is continuous for all real numbers and the graphs of f$^(\text{'})$ and f$^(\text{'}\text{'})$ are given.

$($a$)$ Determine the critical numbers of f$.$

$($Enter your answer rounded to one decimal place. Enter DNE if the solution does not exist. Give your answer in the form of a

comma$-$separated list of numbers.$)$

$($b$)$ Where is f increasing?

$($Enter your answer rounded to one decimal place. Give your answers as intervals in the form $(,).$ Use the symbol oo for

infinity, U for combining intervals, and an appropriate type of parenthesis $"(",")","["$ or $"]"$ depending on whether the interval is

open or closed. Enter O$/$ if the interval is empty.$)$

f is increasing on

$($c$)$ Where is f decreasing?

$($Enter your answer rounded to one decimal place. Give your answers as intervals in the form $(,).$ Use the symbol oo for

infinity, U for combining intervals, and an appropriate type of parenthesis $"(",")","["$ or $"]"$ depending on whether the interval is

open or closed. Enter O$/$ if the interval is empty.$)$

f is decreasing on

$($d$)$ At what numbers x$,$ if any, does f have a local minimum?

$($Enter your answer rounded to one decimal place. Enter DNE if the solution does not exist. Give your answer in the form of a

comma$-$separated list of numbers.$)$

$($e$)$ At what numbers x$,$ if any, does f have a local maximum?

$($Use symbolic notation and fractions where needed. Enter DNE if the solution does not exist. Give your answer in the form of a

comma$-$separated list of numbers.$)$

local maximum at the number$($s$)$:

$($f$)$ Where is f concave up$?$

$($Use symbolic notation and fractions where needed. Give your answers as intervals in the form $(**,**).$ Use the symbol oo for

infinity, U for combining intervals, and an appropriate type of parenthesis $"(",")","["$ or $"]"$ depending on whether the interval is

open or closed. Enter O$/$ if the interval is empty.$)$

f is concave up or

$($g$)$ Where is f concave down?

$($Use symbolic notation and fractions where needed. Give your answers as intervals in the form $(**,**).$ Use the symbol oo for

infinity, U for combining intervals, and an appropriate type of parenthesis $"(",")","["$ or $"]"$ depending on whether the interval is

open or closed. Enter O$/$ if the interval is empty.$)$

$($h$)$ List the x$-$coordinates of any inflection points.

Inflection points are at the number$($s$)$: