# If every convex function is of bounded variation?

The properties of convex functions are of interest. I would like to know that if every convex function is of bounded variation?

No, take $f(x)=e^x$ on $\mathbb R$, or $g(x) = \frac1{x(1-x)}$ on $(0,1)$.
• Why $f(x)=e^x$ is not of bounded variation?