General classes of mistakes people make:

- sloppy
  dropping signs, algebra mistakes, copy errors, etc.
  If you're -organized- and -not sloppy-, you won't make these.

- reversing implications
  If $x$ is a local max/min, and $f$ is differentiable at $x$,
  then $f'(x)=0$; the reverse isn't true.

- forgetting conditions
  ``If $x$ is a local max/min, then $f'(x)=0$?''
  no: $f$ needn't be differentiable at $x$.

- cavalier/wreckless :: ignoring -delicate- statements
  not checking that all conditions are satisfied;
  this is a bit different from the above; I mean stuff like
  switching limits (and integrals, etc.) w/o checking
  for uniform convergence or some such.

- over-generalizing
  ``if $f$ is increasing, then $f'>0$ for all $x$?''
  no: $f'(x)\geq 0$
  (and the reverse implication is trickier: if $f'\geq 0$,
  $f$ needn't be increasing, obviously, though if $f'>0$ it is;
  just need $f'\geq 0$, and only equal $0$ on a set of measure $0$)

- dyslexic: reversing order of quantifiers
  $\forall x \exists \epsilon$
  versus
  $\exists \epsilon \forall x$
  remember, this is -not- common language: we shouldn't
  use commas and switch stuff around.
