Chapter 4.1, Problem 47ES

Use a graphing utility to generate the graphs of $f^{\prime }$ and $f^{″}$ over the stated interval; then use those graphs to estimate the x-coordinates of the inflection points of $f,$ the intervals on which $f$ is concave up or down, and the intervals on which $f$ is increasing or decreasing. Check your estimates by graphing $f$ .

$f\left(x\right)=x^4-24x^2+12x,-5\le x\le 5$