Chapter 9.4, Problem 46E

For each function in Problems 43-46, do the following.

(a) Find. $f\text{'}\left(x\right)$

(b) Graph both $f\left(x\right)$

and $f\text{'}\left(x\right)$ using a graphing calculator.

(c) Use the graph of $f\text{'}\left(x\right)$ to identify x-values where $f\text{'}\left(x\right)=0,f\text{'}\left(x\right)>0,andf\text{'}\left(x\right)<0$.

(d) Use the graph of $f\left(x\right)$ to identify x-values where $f\left(x\right)$ has a maximum or minimum point, where the graph of $f\left(x\right)$ is rising, and where the graph of $f\left(x\right)$ is falling.

$f\left(x\right)=7-3x^2-\frac{x^3}{3}$