Question $3(12$ pts$).$ Consider the function $f$:$[-8,5]R,$

$f(x)=2x^3+3x^2-72x+40$

a$.$ State the set of interior points and boundary points for the domain of $f.$

b$.$ Find all the critical points of $f.($Show your steps.$)$

c$.$ Find all the local min and local max of $f.($Show your steps.$)$

d$.$ Find the global min and max of $f.($Show your steps.$)$

e$.$ Sketch the graph of $f$ on its domain and clearly mark the critical points, boundary points and global max $($min$)$ on the graph.