$(30$ pts$)$ Let $f(x)=x^{3}6x^2-9x8.$

a$.)(10$ pts$)$ Determine the intervals in which $f(x)$ increases and$/$or decreases.

b$.)(5$ pts$)$ Determine any relative extreme values for the function.

c$.)(10$ pts$)$ Determine the intervals in which $f(x)$ is concave up and$/$or concave down.

d$.)(5$ pts$)$ Determine if the function has any points of inflection.