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$.$

$($Give your answer$($s$)$ to one decimal place, if applicable. Enter DNE if the solution does not exist. Give your answer in the form

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

critical numbers

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Give your answers as intervals in the form $(**,**).$ Use the symbol oo

for infinity, u for combining intervals, and parenthesis $"(",")"$ for open intervals. Enter O$/$ if the interval is empty.$)$

f is increasing on:

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Give your answers as intervals in the form $(**,**).$ Use the symbol oo

for infinity, U for combining intervals, and parenthesis $"(",")"$ for open intervals. Enter O$/$ if the interval is empty.$)$

f is decreasing on

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Enter DNE if the solution does not exist. Give your answer in the form

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

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

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

$($Give your answer$($s$)$ to one decimal place, if applicable. 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$?$

$($Give your answer$($s$)$ to one decimal place, if applicable. Give your answers as intervals in the form $(**,**).$ Use the symbol oo

for infinity, U for combining intervals, and parenthesis $"(",")"$ for open intervals. Enter O$/$ if the interval is empty.$)$

f is concave up on

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Give your answers as intervals in the form $(**,**).$ Use the symbol oo

for infinity, U for combining intervals, and parenthesis $"(",")"$ for open intervals. Enter O$/$ if the interval is empty.$)$

f is concave down on

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Enter DNE if the solution does not exist. Give your answer in the form

of a comma$-$separated list of numbers.$)$ The function $\backslash ($ f $\backslash )$ is continuous for all real numbers and the graphs of $\backslash ($ f$^\{\backslash$prime$\}\backslash )$ and $\backslash ($ f$^\{\backslash$prime $\backslash$prime$\}\backslash )$ are given.

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Enter DNE if the solution does not exist. Give your answer in the form of a comma$-$separated list of numbers.$)$

critical numbers

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Give your answers as intervals in the form $(\backslash (*,*\backslash )).$ Use the symbol $\backslash (\backslash$infty $\backslash )$ for infinity, $\backslash ($ u $\backslash )$ for combining intervals, and parenthesis $"(",")"$ for open intervals. Enter $\backslash (\backslash$varnothing $\backslash )$ if the interval is empty.$)$

$\backslash ($ f $\backslash )$ is increasing on $($c$)$ Where is $\backslash ($ f $\backslash )$ decreasing?

$($Give your answer$($s$)$ to one decimal place, if applicable. Give your answers as intervals in the form $(\backslash (*,*\backslash )).$ Use the symbol $\backslash (\backslash$infty $\backslash )$ for infinity, U for combining intervals, and parenthesis $"(",")"$ for open intervals. Enter $\backslash (\backslash$varnothing $\backslash )$ if the interval is empty.$)$

$\backslash ($ f $\backslash )$ is decreasing on

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Enter DNE if the solution does not exist. Give your answer in the form of a comma$-$separated list of numbers.$)$

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

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

$($Give your answer$($s$)$ to one decimal place, if applicable. 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 $\backslash ($ f $\backslash )$ concave up$?$

$($Give your answer$($s$)$ to one decimal place, if applicable. Give your answers as intervals in the form $(\backslash (*,*\backslash )).$ Use the symbol $\backslash (\backslash$infty $\backslash )$ for infinity, U for combining intervals, and parenthesis $"(",")"$ for open intervals. Enter $\backslash (\backslash$varnothing $\backslash )$ if the interval is empty.$)$

$\backslash ($ f $\backslash )$ is concave up on

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Give your answers as intervals in the form $(\backslash (*,*\backslash )).$ Use the symbol $\backslash (\backslash$infty $\backslash )$ for infinity, U for combining intervals, and parenthesis $"(",")"$ for open intervals. Enter $\backslash (\backslash$varnothing $\backslash )$ if the interval is empty.$)$

$\backslash ($ f $\backslash )$ is concave down on

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

$($Give your answer$($s$)$ to one decimal place, if applicable. Enter DNE if the solution does not exist. Give your answer in the form of a comma$-$separated list of numbers.$)$