Consider the following function.

$f(x)=4x^3+6x^2-24x+2$

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

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

$($b$)$ Find the local minimum and maximum values of $f.$

local minimum value $$

local maximum value $$

$($c$)$ Find the inflection point.

$$

$(x,y)=()$

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

$$

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