Consider the function $(x)=x^4-8x^3+18x^2-27,$ and in factored form: $f(x)=(x+1)(x-3{)}^3$

a$)$ Determine the $x$ and $y-$intercepts.

b$)$ Determine the coordinates and nature of the critical points.

c$)$ Determine the intervals of increase and decrease.

d$)$ Determine the coordinates of the inflection points.

e$)$ Determine the intervals of concavity.

f$)$ Graph the function on the grid below. $($Label axes appropriately$)$

Label each part of this question clearly! Use extra paper if needed but include them in your scan.