DERIVATIVES AND GRAPHS

If f'(x)<0 on an interval then f is increasing on that interval

A critical number of a function f is a number c in the domain of f such that either f'(x)=0 or f'(x) does not exist.

If f has a local maximum or minimum at c then c is a critical number of f

If f'(x) does not change signs at c, then:

If f'(x) changes from positive to negative at c then f has a local minimum at c.