Chapter 4, Problem 10RE

In Problems 9 and 10, use the given information to sketch the graph off. Assume that f is continuous on its domain and that all intercepts are included in the information given.

10. Domain: All real x

     $f\left(-2\right)=1,f\left(0\right)=0,f\left(2\right)=1;$

     $f^{\prime }\left(0\right)=0;f^{\prime }\left(x\right)<0\text{on}\left(-\infty ,0\right);$

     $f^{\prime }\left(x\right)>0\text{on}\left(0,\infty \right);$

     $f^{″}\left(-2\right)=0,f^{″}\left(2\right)=0;$

     $f^{″}(x)<0on\left(-\infty ,-2\right)\text{and}\left(2,\infty \right);$

     $f^{″}\left(x\right)>0\text{on}\left(-2,2\right);$

     $\underset{x\to -\infty }{\lim }f\left(x\right)=2;\underset{x\to \infty }{\lim }f\left(x\right)=2$