Chapter 4.4, Problem 38E

To determine

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

  $\begin{array}{l}f\left(x\right)=x\text{ if }x=-1,2,4,8\\ f^{\text{'}}\left(x\right)=0\text{ if }x=-1,4,6,8\\ f^{\text{'}}\left(x\right)<0\text{ throughout }\left(-\infty ,-1\right),\left(4,6\right)\text{ and }\left(8,\infty \right)\\ f^{\text{'}}\left(x\right)>0\text{ throughout }\left(-1,4\right)\text{ and }\left(6,8\right)\\ f^{\text{'}\text{'}}\left(x\right)>0\text{ throughout }\left(-\infty ,0\right),\left(2,3\right)\text{ and }\left(5,7\right)\\ f^{\text{'}\text{'}}\left(x\right)<0\text{ throughout }\left(0,2\right),\left(3,5\right)\text{ and }\left(7,\infty \right)\end{array}$