# What do critical points tell you?

Fermat's Theorem tells us that: if a function, $f$ has a relative extremum at $c$ (If $f \left(c\right)$ is a relative extremum), the either $f ' \left(c\right) = 0$ or $f ' \left(c\right)$ does not exist.
A critical point is a point in the domain (so we know that $f$ does have some value there) where one of the conditions: $f ' \left(c\right) = 0$ or $f ' \left(c\right)$ does not exist, is satisfied.
If $f$ has any relative extrema, they must occur at critical points.