Chapter 3.3, Problem 29E

Suppose f is a continuous function where $f\left(x\right)>0$ for all x,

$\begin{array}{l}f\left(0\right)=4,f\prime \left(x\right)>0\text{ if }x<0\text{ or }x>2,f\prime \left(x\right)<0\\ \text{if }0<x<2,f\prime \prime \left(-1\right)=f\prime \prime \left(1\right)=0,f\prime \prime \left(x\right)>0\text{ if}\\ x<-1\text{ or }x>1,f\prime \prime \left(x\right)<0\text{ if }-1<x<1.\end{array}$

(a) Can f have an absolute maximum? If so, sketch a possible graph of f, If not, explain why.

(b) Can f have an absolute minimum? If so, sketch a possible graph of f. If not, explain why.

(c) Sketch a possible graph for f that does not achieve an absolute minimum.