Critical number & maximum and minimum values
Intros
Lessons
- local maximum local minimum critical number
- state the: absolute maximum absolute minimum
- on the interval,
state the: absolute maximum absolute minimum
Examples
Lessons
- Find the critical numbers of the function:
- First Derivative Test: a test to determine whether or not has a local maximum or minimum at a critical number
First Derivative Test
local maximum
local minimum
no maximum or minimum
no maximum or minimum
- The Closed Interval Method To find the absolute maximum and minimum values of a continuous function on a closed interval [a, b]: 1.Find the values of at the critical numbers of in (a, b). 2.Find the values of at the left-endpoint and right-endpoint of the interval 3.Compare all values from steps 1 and 2: the largestis the absolute maximum value; the smallestis the absolute minimum value.
- Find the absolute maximum and minimum values of the function: