Chapter 9.6, Problem 31E

In Problems 31 and 32, do the following for each function $f\left(x\right)$.

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

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

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

(c) Determine x-values where $f\text{'}\left(x\right)=0,f\text{'}\left(x\right)>0,f\text{'}\left(x\right)<0$.

(d) Determine x-values for which $f\left(x\right)$ has a maximum or minimum point, where the graph is increasing, and where it is decreasing.

$f(x)=12-3{\left(1-x^2\right)}^{4/3}$