Consider the function f$($x$)=$ x $+6$x$^2/3$

$($f$)$ Give the inflection points of f$($x$).$

Enter your answers in increasing order of the x$-$coordinate. If there are less than two points of

inflection, enter NA in the remaining response areas.

Include a multiplication sign between symbols. For example, a$*$pi$.($c$)$ Give the intervals of increase and decrease of $\backslash ($ f$($x$)\backslash ).$

Note: Use the letter $\backslash ($ U $\backslash )$ for union. To enter $\backslash (\backslash$infty $\backslash ),$ type infinity with a lower case i$.$

If the function is never increasing or decreasing, enter NA in the associated response area.

increasing:

decreasing:

$($c$)$ Give the intervals of increase and decrease of $\backslash ($ f$($x$)\backslash ).$

Note: Use the letter $\backslash ($ U $\backslash )$ for union. To enter $\backslash (\backslash$infty $\backslash ),$ type infinity with a lower case i$.$

If the function is never increasing or decreasing, enter NA in the associated response area.

increasing:

decreasing:

$($c$)$ Give the intervals of increase and decrease of $\backslash ($ f$($x$)\backslash ).$

Note: Use the letter $\backslash ($ U $\backslash )$ for union. To enter $\backslash (\backslash$infty $\backslash ),$ type infinity with a lower case i$.$

If the function is never increasing or decreasing, enter NA in the associated response area.

increasing:

decreasing:

$($d$)$ Give the local maximum and minimum values of $\backslash ($ f$($x$)\backslash ).$

Enter your answers in increasing order of the $\backslash ($ x $\backslash )-$value. If there are less than two local extrema enter NA in the remaining response areas and the corresponding drop$-$down menu.

Include a multiplication sign between symbols. For example, $\backslash ($ a $\backslash$cdot $\backslash$pi $\backslash ).($e$)$ Give the intervals of concavity of $\backslash ($ f$($x$)\backslash ).$

Note: Use the letter $\backslash ($ U $\backslash )$ for union. To enter $\backslash (\backslash$infty $\backslash ),$ type infinity with a lower case i$.$

If the function is never concave upward or concave downward, enter NA in the associated response area.

concave

upward:

concave

downward: