Identifying Absolute Extrema Concepts

Graphing functions

Identifying absolute extrema

Finding relative extrema

Understanding derivatives

A point where the function has a minimum value

A point where the function has a maximum value

A point where the derivative is zero or undefined

A point where the function is undefined

Only the critical points

Only the endpoints

Both critical points and endpoints

Neither critical points nor endpoints

f(x) = x^2 + 3x - 1

f(x) = x^2 - 3x + 1

f(x) = x^3 - 3x^2 + 1

f(x) = x^3 + 3x^2 - 1

Five

Four

Three

Two

1

0.125

-3

17

To graph the function

To find the derivative

To quickly calculate function values

To solve equations

f is increasing

f has a maximum

f is constant

f is decreasing

An absolute minimum

A relative maximum

An absolute maximum

A relative minimum

To highlight critical points

To visualize increasing and decreasing intervals

To identify endpoints

To calculate derivatives