Attempt $2$: $0$ out of $4$ parts have been answered correctly.

Below is the graph of the derivative $\backslash ($ f$^\{\backslash$prime$\}($x$)\backslash )$ of a function defined on the interval $\backslash ((0,8)\backslash ).$ You can click on the graph to see a larger version in a separate window.

Refer to the graph to answer each of the following questions. For parts $($A$)$ and $($B$),$ use interval notation to report your answer. $($If needed, you use $\backslash (\backslash$mathbf$\{$U$\}\backslash )$ for the union symbol.$)$

$($A$)$ For what values of $\backslash ($ x $\backslash )$ in $\backslash ((0,8)\backslash )$ is $\backslash ($ f$($x$)\backslash )$ increasing? $($If the function is not increasing anywhere, enter None $.)$

Answer:

$($B$)$ For what values of $\backslash ($ x $\backslash )$ in $\backslash ((0,8)\backslash )$ is $\backslash ($ f$($x$)\backslash )$ concave down? $($If the function is not concave down anywhere, enter None $.)$

Answer:

$($C$)$ Find all values of $\backslash ($ x $\backslash )$ in $\backslash ((0,8)\backslash )$ is where $\backslash ($ f$($x$)\backslash )$ has a local minimum, and list them $($separated by commas$)$ in the box below. $($If there are no local minima, enter None $.)$

Local Minima:

$($D$)$ Find all values of $\backslash ($ x $\backslash )$ in $\backslash ((0,8)\backslash )$ is where $\backslash ($ f$($x$)\backslash )$ has an inflection point, and list them $($separated by commas$)$ in the box below. $($If there are no inflection points, enter None $.)$

Inflection Points: