Consider the equation below.

$f(x)=2x^3+3x^2-72x$

$(a)$ Find the interval$(s)of$ increase. $(Enter$ your answer $in$ interval notation.$)$

Find the interval$(s)of$ decrease. $(Enter$ your answer $in$ interval notation.$)$

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

local minimum

local maximum

$(c)$ Find the inflection point.

$(x,y)=(,)$

Find the interval $on$ which $fis$ concave $up.(Enter$ your answer $in$ interval notation.$)$

Find the interval $on$ which $fis$ concave down. $(Enter$ your answer $in$ interval notation.$)$