Consider the equation below. $($If an answer does not exist, enter DNE.$)$

f$($x$)=$ x$48$x$2+7$

$($a$)$

Find the interval on which f is increasing. $($Enter your answer using interval notation.$)$

$(2,0)(2,$$)$

Find the interval on which f is decreasing. $($Enter your answer using interval notation.$)$

$($$,2)(0,2)$

$($b$)$

Find the local maximum and minimum values of f$.$

local minimum value

x$=1,5$

local maximum value

x$=0$

$($c$)$

Find the inflection points. $($Order your answers from smallest to largest x$,$ then from smallest to largest y$.)$

$($x$,$ y$)$

$=$

$(1\mathrm{.}155,6\mathrm{.}0)$

$($x$,$ y$)$

$=$

$(1\mathrm{.}155,6\mathrm{.}0)$

Find the interval on which f is concave up$.($Enter your answer using interval notation.$)$

$($$,1\mathrm{.}155)(1\mathrm{.}155,$$)$

Find the interval on which f is concave down.$($Enter your answer using interval notation.$)$

$(1\mathrm{.}155,1\mathrm{.}155)$