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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!

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.

Locate extrema candidates where . Remember to only consider candidates within the given domain: .


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

Three extrema candidates have been identified.

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

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