Flashcard #3 - Derivatives Part A (1st & 2nd Derivative Tests)

A critical point is a point where

f’ (x) = 0

or where f’ (x) is undefined

The first derivative test tells us that a function will be increasing when

f’ > 0

The first derivative test tells us that a function will be decreasing when

f’ < 0

We are guaranteed that a function will have an absolute maximum and absolute minimum value if

The function is continuous on a closed interval

Absolute maximum and absolute minimum points will occur at

The endpoints of a closed interval or at critical points

An inflection point is a point where

f’’ changes sign and f’’ = 0

A function is concave up when

f’’ > 0

A function is concave down when

f’’ < 0

Horizontal tangents to a curve will occur where

f’ = 0

If f’ changes from positive to negative at a critical point c then f has a ___ at c

Local Maximum

If f’ changes from negative to positive at a critical point c then f has a ___ at c

Local Minimum