PLEASE SHOW ALL WORK. $(22$ points$)$ Sketch the graph of this function using the following guidelines:

$f(x)=x^3-3x$

a$)$ Intercept$($s$),$ if any:

b$)$ Increasing and decreasing intervals:

c$)$ Local Maximum and Minimum Point$($s$)$:

Increasing interval $=$

Decreasing interval $=$

Local Maximum Point $=$

Local Minimum Point $=$

Concave up interval $=$

Concave down interval $=$

e$)$ Inflection Point$($s$),$ if any:

Inflection Point $=$

f$)$ Graph:

$4$