Chapter 4.4, Problem 13E

Let $f\left(x\right)=\left(x-3\right){\left(x+3\right)}^2$.

a.    Verify that $f^{\prime }\left(x\right)=3\left(x-1\right)\left(x+3\right)$ and $f^{″}\left(x\right)=6\left(x+1\right)$.

b.    Find the critical points and possible inflection points of f.

c.    Find the intervals on which f is increasing or decreasing.

d.    Determine the intervals on which f is concave up or concave down.

e.    Identify the local extreme values and inflection points of f.

f.    State the x- and y-intercepts of the graph of f.

g.    Use your work in parts (a) through (f) to sketch a graph of f.