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6-63.

Write the first and second derivatives for the function below and use them to test for extrema over the given interval. Remember to check the endpoints! Homework Help ✎

This problem is asking you to find EXTREME VALUES on a closed domain.
Extreme values (global maxima and global minima) can exist where or where DNE.

Math Notes for Extreme Values

Locate extrema candidates where y' = 0. Remember to only consider candidates within the given domain: [0, π].


Locate more extrema candidates where y' = DNE. In other words, where is y non-differentiable? Are there endpoints, jumps, holes, cusps, or vertical tangents? If so, these are extrema candidates. There are endpoint candidates at and .

5 graphs

Three extrema candidates have been identified.

Test each candidate to see who has the most extreme (highest and lowest) y-values.
The 'winners' are the global max and the global min.

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