Find the first and second derivatives and use them to test for maxima and minima on 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
Find extrema candidates where
Find more extrema candidates where
Test each candidate to see who has the most extreme (highest and lowest)
The 'winners' are the global max and the global min.