If we have 2 monotone functions $f$ and $g$ non zero, is it possible that $fg$ has more than one turning point. We can assume wlog that $f$ is increasing and $g$ is decreasing. $\frac{1}{x}e^x$ is an example of one turning point but I can't think of any examples of more than one turning point. Does one exist?
Also if it does, what if we enforce a linear bound on the increasing function?
Thanks.