Critical number & maximum and minimum values
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Intros
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: