Chapter 4.4, Problem 35E

To determine

To Sketch: The graph of a continuous function $f$ that satisfies all the stated conditions:

  $\begin{array}{l}f\left(-2\right)=f\left(6\right)=-2;f\left(0\right)=f\left(4\right)=0;f\left(2\right)=f\left(8\right)=3;\\ f^{\text{'}}\left(x\right)\text{ is undefined at }x=2,6.f^{\text{'}}\left(0\right)=1\\ f^{\text{'}}\left(x\right)>0\text{ throughout }\left(-\infty ,2\right)\text{ and }\left(6,\infty \right);\\ f^{\text{'}}\left(x\right)<0\text{ if }\left|x-4\right|<2;\\ f^{\text{'}\text{'}}\left(x\right)<0\text{ throughout }\left(-\infty ,0\right),\left(4,6\right)\text{ and }\left(6,\infty \right);\\ f^{\text{'}\text{'}}\left(x\right)>0\text{ throughout }\left(0,2\right)\text{ and }\left(2,4\right).\end{array}$