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Home > CALC > Chapter 5 > Lesson 5.5.1 > Problem 5-154


Without using a graphing calculator, find the maximum and minimum values of the function on the interval .

Candidates for global maxima and global minima exist where the derivative equals AND where the derivative does not exist.... Notice that this is a function that has a closed domain. That means that we already know two candidates for global max and min: the endpoints.

Evaluate the endpoints:

These might be the global min and max, respectively. We still need to check the other candidates.

Find additional candidates by setting the derivative equal to zero, and solving for .

, and are candidates...
but eliminate because it is not within the given domain.

Evaluate the remaining candidates: , and compare to the endpoint candidates.

Recall that maxima and minima are -values.
Therefore the global maximum is and the global minimum is .It should also be noted that is a local maximum.
Confirm this by sketching on your graphing calculator.