\caution{Common misconceptions:
- if $f$ is increasing, then $f'(x) > 0$ for all $x$
  Correct statement:
  - if $f$ is \emph{non-decreasing}, then $f'(x) \geq 0$ for all $x$
  Counter-example to bear in mind: $x^3$; increasing, but $f'(0)=0$

- if $f$ is increasing on the whole real line, then it goes off to $+\infty$
  (as $x \to +\infty$) and $-\infty$ (as $x \to -\infty$)
  Just false: you may have an asymptote
  Examples: $\arctan x$ and $\log x$
    (can look at $\int_0^x f'$ to see what happens)}
