Question

What do critical points tell you?

Answer 1

A critical point for a function is a place where the function might have a relative extremum. (Also called a "local" , extreme or extreme value)

Fermat's Theorem tells us that: if a function, `f` has a relative extremum at `c` (If `f(c)` is a relative extremum), the either `f'(c)=0` or `f'(c)` 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'(c)=0` or `f'(c)` does not exist, is satisfied.

If `f` has any relative extrema, they must occur at critical points.