Chapter 2.1, Problem 24E

Sketch the graph of a function g for which $g\left(0\right)=g\left(2\right)=g\left(4\right)=0$, $g\prime \left(1\right)=g\prime \left(3\right)=0$, $g\prime \left(0\right)=g\prime \left(4\right)=1$, $g\prime \left(2\right)=-1$, ${\lim }_{x\to 5^{-}}g\left(x\right)=\infty$, and ${\lim }_{x\to -1^{+}}g\left(x\right)=-\infty$.