Consider the following.

$f(x)=3x^3-9x^2-135x$

$($a$)$ Find the intervals on which $f$ is increasing or decreasing. $($Enter your answers using interval notation.$)$

increasing

decreasing

$($b$)$ Find the local maximum and minimum values of $f.($If an answer does not exist, enter DNE.$)$

local minimum value

local maximum value

$($c$)$ Find the intervals of concavity and the inflection points. $($Enter your answers using interval notation.$)$

concave up

concave down

inflection point $,(x,y)=(,)$Consider the following.

$f(x)=x^4-8x^2+1$

$($a$)$ Find the intervals on which $f$ is increasing or decreasing. $($Enter your answers using interval notation.$)$

increasing

decreasing

$($b$)$ Find the local maximum and minimum values of $f.($If an answer does not exist, enter DNE.$)$

local minimum value

local maximum value

$($c$)$ Find the intervals of concavity and the inflection points. $($Enter your answers using interval notation.$)$

concave up

concave down

inflection point $,(x,y)=(,)($smaller $x-$value$)$

inflection point $,(x,y)=(,)($larger $x-$value$)$