Question: Sketch the graph of \[f(x)={{x}^{3}}-9{{x}^{2}}+72\] using the second derivative test.

a). determine the domain

b). determine the intervals where the function is increasing and decreasing

c). determine the inflection point(s)

d). determine the intervals where the function is concave up or concave down

e). determine relative max and relative min point(s)

f). graph the function