Chapter 3.3, Problem 26E

20-27 Sketch the graph of a function that satisfies all of the given conditions.

$\begin{array}{l}f\prime \left(0\right)=f\prime \left(4\right)=0,f\prime \left(x\right)=1\text{ if }x<-1,\\ f\prime \left(x>\right)>0\text{ if }0<x<2,\\ f\prime \left(x\right)<0\text{ if }-1<x<0\text{ or 2}<x<4\text{ or }x>4,\\ \underset{x\to 2^{-}}{\lim }f\prime \left(x\right)=\infty ,\underset{x\to 2^{+}}{\lim }f\prime \left(x\right)=-\infty \\ f\prime \prime \left(x\right)>0\text{ if }-1<x<2\text{ or 2}<x<4,\\ f\prime \prime \left(x\right)<0\text{ if }x>4\end{array}$