Consider the following. $(Ifan$ answer does not exist, enter DNE.$)$

$f(x)=2x^3-6x^2+5$

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

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

$(b)$ Find the local minimum value$(s).(Enter$ your answers $as$ a comma$-$separated list.$)$

Find the local maximum value$(s).(Enter$ your answers $as$ a comma$-$separated list.$)$

$(c)$ Find the inflection point.

$\{$:$(x,y)={|}_{\text{d}\text{a}\text{r}\text{r}})$

Find the interval$(s)$ where the function $is$ concave $up.(Enter$ your answer using interval notation.$)$

Find the interval$(s)$ where the function $is$ concave down. $(Enter$ your answer using interval notation.$)$